Book Review
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John W. Aaber and Nathan Dunfield, Closed surface bundles of least volume, Algebr. Geom. Topol. 10 (2010), no. 4, 2315–2342. MR 2745673, DOI 10.2140/agt.2010.10.2315
William Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Mathematics, vol. 820, Springer, Berlin, 1980. MR 590044
Ian Agol, The virtual haken conjecture, arXiv:1204.2810.
Ian Agol, Ideal triangulations of pseudo-Anosov mapping tori, Topology and geometry in dimension three, Contemp. Math., vol. 560, Amer. Math. Soc., Providence, RI, 2011, pp. 1–17. MR 2866919, DOI 10.1090/conm/560/11087
Pierre Arnoux and Jean-Christophe Yoccoz, Construction de difféomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 1, 75–78 (French, with English summary). MR 610152
D. Asimov and J. Franks, Unremovable closed orbits, Geometric dynamics (Rio de Janeiro, 1981) Lecture Notes in Math., vol. 1007, Springer, Berlin, 1983, pp. 22–29. MR 730260, DOI 10.1007/BFb0061407
Max Bauer, Examples of pseudo-Anosov homeomorphisms, Trans. Amer. Math. Soc. 330 (1992), no. 1, 333–359. MR 1094557, DOI 10.1090/S0002-9947-1992-1094557-8
Max Bauer, An upper bound for the least dilatation, Trans. Amer. Math. Soc. 330 (1992), no. 1, 361–370. MR 1094556, DOI 10.1090/S0002-9947-1992-1094556-6
Lipman Bers, An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), no. 1-2, 73–98. MR 477161, DOI 10.1007/BF02545743
M. Bestvina and M. Handel, Train-tracks for surface homeomorphisms, Topology 34 (1995), no. 1, 109–140. MR 1308491, DOI 10.1016/0040-9383(94)E0009-9
Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281
Joan S. Birman and Mark E. Kidwell, Fixed points of pseudo-Anosov diffeomorphisms of surfaces, Adv. in Math. 46 (1982), no. 2, 217–220. MR 679909, DOI 10.1016/0001-8708(82)90024-X
Joan S. Birman, Alex Lubotzky, and John McCarthy, Abelian and solvable subgroups of the mapping class groups, Duke Math. J. 50 (1983), no. 4, 1107–1120. MR 726319, DOI 10.1215/S0012-7094-83-05046-9
Francis Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988), no. 1, 139–162. MR 931208, DOI 10.1007/BF01393996
Philip Boyland, Notes on dynamics of surface homeomorphisms, Warwick, preprint.
Peter Brinkmann, An implementation of the Bestvina-Handel algorithm for surface homeomorphisms, Experiment. Math. 9 (2000), no. 2, 235–240. MR 1780208
Peter Brinkmann, A note on pseudo-Anosov maps with small growth rate, Experiment. Math. 13 (2004), no. 1, 49–53. MR 2065567
John Cantwell and Lawrence Conlon, Handel–Miller theory and finite depth foliations, arXiv:1006.4525.
Andrew J. Casson and Steven A. Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Mathematical Society Student Texts, vol. 9, Cambridge University Press, Cambridge, 1988. MR 964685, DOI 10.1017/CBO9780511623912
Jin-Hwan Cho and Ji-Young Ham, The minimal dilatation of a genus-two surface, Experiment. Math. 17 (2008), no. 3, 257–267. MR 2455699
François Dahmani, Vincent Guirardel, and Denis Osin, Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces, arXiv:1111.7048v3.
André de Carvalho, Toby Hall, and Rupert Venzke, On period minimal pseudo-Anosov braids, Proc. Amer. Math. Soc. 137 (2009), no. 5, 1771–1776. MR 2470836, DOI 10.1090/S0002-9939-08-09709-8
Benson Farb (ed.), Problems on mapping class groups and related topics, Proceedings of Symposia in Pure Mathematics, vol. 74, American Mathematical Society, Providence, RI, 2006. MR 2251041, DOI 10.1090/pspum/074
Benson Farb, Some problems on mapping class groups and moduli space, Problems on mapping class groups and related topics, Proc. Sympos. Pure Math., vol. 74, Amer. Math. Soc., Providence, RI, 2006, pp. 11–55. MR 2264130, DOI 10.1090/pspum/074/2264130
Benson Farb, Christopher J. Leininger, and Dan Margalit, The lower central series and pseudo-Anosov dilatations, Amer. J. Math. 130 (2008), no. 3, 799–827. MR 2418928, DOI 10.1353/ajm.0.0005
Benson Farb, Christopher J. Leininger, and Dan Margalit, Small dilatation pseudo-Anosov homeomorphisms and 3-manifolds, Adv. Math. 228 (2011), no. 3, 1466–1502. MR 2824561, DOI 10.1016/j.aim.2011.06.020
Benson Farb and Dan Margalit, A primer on mapping class groups, Princeton Mathematical Series, vol. 49, Princeton University Press, Princeton, NJ, 2012. MR 2850125
Albert Fathi, Démonstration d’un théorème de Penner sur la composition des twists de Dehn, Bull. Soc. Math. France 120 (1992), no. 4, 467–484 (French, with English and French summaries). MR 1194272
Sérgio R. Fenley, End periodic surface homeomorphisms and $3$-manifolds, Math. Z. 224 (1997), no. 1, 1–24. MR 1427700, DOI 10.1007/PL00004576
John Franks and Michael Handel, Periodic points of Hamiltonian surface diffeomorphisms, Geom. Topol. 7 (2003), 713–756. MR 2026545, DOI 10.2140/gt.2003.7.713
David Fried, Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helv. 57 (1982), no. 2, 237–259. MR 684116, DOI 10.1007/BF02565860
David Fried, Growth rate of surface homeomorphisms and flow equivalence, Ergodic Theory Dynam. Systems 5 (1985), no. 4, 539–563. MR 829857, DOI 10.1017/S0143385700003151
Koji Fujiwara, Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents, arXiv:0908.0995.
Jean-Marc Gambaudo, Sebastian van Strien, and Charles Tresser, Vers un ordre de Sarkovskiĭ pour les plongements du disque préservant l’orientation, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 5, 291–294 (French, with English summary). MR 1042866
Marlies Gerber and Anatole Katok, Smooth models of Thurston’s pseudo-Anosov maps, Ann. Sci. École Norm. Sup. (4) 15 (1982), no. 1, 173–204. MR 672479
Ji-Young Ham and Won Taek Song, The minimum dilatation of pseudo-Anosov 5-braids, Experiment. Math. 16 (2007), no. 2, 167–179. MR 2339273
Michael Handel, Global shadowing of pseudo-Anosov homeomorphisms, Ergodic Theory Dynam. Systems 5 (1985), no. 3, 373–377. MR 805836, DOI 10.1017/S0143385700003011
Michael Handel, The forcing partial order on the three times punctured disk, Ergodic Theory Dynam. Systems 17 (1997), no. 3, 593–610. MR 1452182, DOI 10.1017/S0143385797084940
Michael Handel and Richard Miller, Handel–Miller theory and finite depth foliations, unpublished.
Michael Handel and William P. Thurston, New proofs of some results of Nielsen, Adv. in Math. 56 (1985), no. 2, 173–191. MR 788938, DOI 10.1016/0001-8708(85)90028-3
John L. Harer, The cohomology of the moduli space of curves, Theory of moduli (Montecatini Terme, 1985) Lecture Notes in Math., vol. 1337, Springer, Berlin, 1988, pp. 138–221. MR 963064, DOI 10.1007/BFb0082808
Eriko Hironaka, Small dilatation mapping classes coming from the simplest hyperbolic braid, Algebr. Geom. Topol. 10 (2010), no. 4, 2041–2060. MR 2728483, DOI 10.2140/agt.2010.10.2041
Eriko Hironaka and Eiko Kin, A family of pseudo-Anosov braids with small dilatation, Algebr. Geom. Topol. 6 (2006), 699–738. MR 2240913, DOI 10.2140/agt.2006.6.699
N. V. Ivanov, Nielsen numbers of mappings of surfaces, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 122 (1982), 56–65, 163–164 (Russian, with English summary). Studies in topology, IV. MR 661465
N. V. Ivanov, Coefficients of expansion of pseudo-Anosov homeomorphisms, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 167 (1988), no. Issled. Topol. 6, 111–116, 191 (Russian, with English summary); English transl., J. Soviet Math. 52 (1990), no. 1, 2819–2822. MR 964259, DOI 10.1007/BF01099245
Nikolai V. Ivanov, Subgroups of Teichmüller modular groups, Translations of Mathematical Monographs, vol. 115, American Mathematical Society, Providence, RI, 1992. Translated from the Russian by E. J. F. Primrose and revised by the author. MR 1195787, DOI 10.1090/mmono/115
Nikolai V. Ivanov, Mapping class groups, Handbook of geometric topology, North-Holland, Amsterdam, 2002, pp. 523–633. MR 1886678
Nikolai V. Ivanov, Fifteen problems about the mapping class groups, Problems on mapping class groups and related topics, Proc. Sympos. Pure Math., vol. 74, Amer. Math. Soc., Providence, RI, 2006, pp. 71–80. MR 2264532, DOI 10.1090/pspum/074/2264532
B. Kolev, Periodic orbits of period $3$ in the disc, Nonlinearity 7 (1994), no. 3, 1067–1071. MR 1275541
Irwin Kra, On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981), no. 3-4, 231–270. MR 611385, DOI 10.1007/BF02392465
Erwan Lanneau and Jean-Luc Thiffeault, On the minimum dilatation of braids on punctured discs, Geom. Dedicata 152 (2011), 165–182. Supplementary material available online. MR 2795241, DOI 10.1007/s10711-010-9551-2
Erwan Lanneau and Jean-Luc Thiffeault, On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 1, 105–144 (English, with English and French summaries). MR 2828128, DOI 10.5802/aif.2599
Christopher J. Leininger, On groups generated by two positive multi-twists: Teichmüller curves and Lehmer’s number, Geom. Topol. 8 (2004), 1301–1359. MR 2119298, DOI 10.2140/gt.2004.8.1301
Darren D. Long and Ulrich Oertel, Hyperbolic surface bundles over the circle, Progress in knot theory and related topics, Travaux en Cours, vol. 56, Hermann, Paris, 1997, pp. 121–142. MR 1603150
Jérôme Los, On the forcing relation for surface homeomorphisms, Inst. Hautes Études Sci. Publ. Math. 85 (1997), 5–61. MR 1471865
Joseph Maher, Random walks on the mapping class group, Duke Math. J. 156 (2011), no. 3, 429–468. MR 2772067, DOI 10.1215/00127094-2010-216
Johanna Mangahas, A recipe for short word pseudo-anosovs, To appear.
Howard Masur, Ergodic actions of the mapping class group, Proc. Amer. Math. Soc. 94 (1985), no. 3, 455–459. MR 787893, DOI 10.1090/S0002-9939-1985-0787893-5
Shigenori Matsumoto, Topological entropy and Thurston’s norm of atoroidal surface bundles over the circle, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), no. 3, 763–778. MR 927609
John McCarthy, A “Tits-alternative” for subgroups of surface mapping class groups, Trans. Amer. Math. Soc. 291 (1985), no. 2, 583–612. MR 800253, DOI 10.1090/S0002-9947-1985-0800253-8
Curtis T. McMullen, Polynomial invariants for fibered 3-manifolds and Teichmüller geodesics for foliations, Ann. Sci. École Norm. Sup. (4) 33 (2000), no. 4, 519–560 (English, with English and French summaries). MR 1832823, DOI 10.1016/S0012-9593(00)00121-X
D. B. McReynolds, The congruence subgroup problem for braid groups: Thurston’s proof, arXiv:0901.4663.
Richard T. Miller, Geodesic laminations from Nielsen’s viewpoint, Adv. in Math. 45 (1982), no. 2, 189–212. MR 664623, DOI 10.1016/S0001-8708(82)80003-0
Hiroyuki Minakawa, Examples of pseudo-Anosov homeomorphisms with small dilatations, J. Math. Sci. Univ. Tokyo 13 (2006), no. 2, 95–111. MR 2277516
Lee Mosher, MSRI course on Mapping Class Groups, Lecture notes (Fall 2007, available at http://andromeda.rutgers.edu/~mosher).
Jakob Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, Acta Math. 50 (1927), no. 1, 189–358 (German). MR 1555256, DOI 10.1007/BF02421324
Jakob Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. II, Acta Math. 53 (1929), no. 1, 1–76 (German). MR 1555290, DOI 10.1007/BF02547566
Jakob Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. III, Acta Math. 58 (1932), no. 1, 87–167 (German). MR 1555345, DOI 10.1007/BF02547775
Jakob Nielsen, Surface transformation classes of algebraically finite type, Danske Vid. Selsk. Mat.-Fys. Medd. 21 (1944), no. 2, 89. MR 15791
Jean-Pierre Otal, Le spectre marqué des longueurs des surfaces à courbure négative, Ann. of Math. (2) 131 (1990), no. 1, 151–162 (French). MR 1038361, DOI 10.2307/1971511
Robert C. Penner, A construction of pseudo-Anosov homeomorphisms, Trans. Amer. Math. Soc. 310 (1988), no. 1, 179–197. MR 930079, DOI 10.1090/S0002-9947-1988-0930079-9
R. C. Penner, Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991), no. 2, 443–450. MR 1068128, DOI 10.1090/S0002-9939-1991-1068128-8
Gérard Rauzy, Échanges d’intervalles et transformations induites, Acta Arith. 34 (1979), no. 4, 315–328 (French). MR 543205, DOI 10.4064/aa-34-4-315-328
Igor Rivin, Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphisms, Duke Math. J. 142 (2008), no. 2, 353–379. MR 2401624, DOI 10.1215/00127094-2008-009
Hongbin Sun, A transcendental invariant of pseudo-anosov maps, arXiv:1209.2613.
William P. Thurston, A discussion on geometrization, Lecture, Harvard University, available at http://www.youtube.com/watch?v=Qzxk8VLqGcI. Video recording by Danny Calegari.
—, Entropy in dimension one, unpublished.
—, Hyperbolic structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle, arXiv:math.GT/9801045, 1986.
William P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357–381. MR 648524, DOI 10.1090/S0273-0979-1982-15003-0
William P. Thurston, A norm for the homology of $3$-manifolds, Mem. Amer. Math. Soc. 59 (1986), no. 339, i–vi and 99–130. MR 823443
William P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 2, 417–431. MR 956596, DOI 10.1090/S0273-0979-1988-15685-6
Chia-Yen Tsai, The asymptotic behavior of least pseudo-Anosov dilatations, Geom. Topol. 13 (2009), no. 4, 2253–2278. MR 2507119, DOI 10.2140/gt.2009.13.2253
William A. Veech, The Teichmüller geodesic flow, Ann. of Math. (2) 124 (1986), no. 3, 441–530. MR 866707, DOI 10.2307/2007091
Kim Whittlesey, Normal all pseudo-Anosov subgroups of mapping class groups, Geom. Topol. 4 (2000), 293–307. MR 1786168, DOI 10.2140/gt.2000.4.293
Daniel Wise, The structure of groups with a quasiconvex hierarchy, preprint.
References
- John W. Aaber and Nathan Dunfield, Closed surface bundles of least volume, Algebr. Geom. Topol. 10 (2010), no. 4, 2315–2342. MR 2745673 (2012c:57030), DOI 10.2140/agt.2010.10.2315
- William Abikoff, The real analytic theory of Teichmüller space, Lecture Notes in Mathematics, vol. 820, Springer, Berlin, 1980. MR 590044 (82a:32028)
- Ian Agol, The virtual haken conjecture, arXiv:1204.2810.
- —, Ideal triangulations of pseudo-Anosov mapping tori, Topology and geometry in dimension three, Contemp. Math., vol. 560, Amer. Math. Soc., Providence, RI, 2011, pp. 1–17. MR 2866919 (2012m:57026)
- Pierre Arnoux and Jean-Christophe Yoccoz, Construction de difféomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 1, 75–78 (French, with English summary). MR 610152 (82b:57018)
- D. Asimov and J. Franks, Unremovable closed orbits, Geometric dynamics (Rio de Janeiro, 1981) Lecture Notes in Math., vol. 1007, Springer, Berlin, 1983, pp. 22–29. MR 730260 (86a:58083), DOI 10.1007/BFb0061407
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- Max Bauer, An upper bound for the least dilatation, Trans. Amer. Math. Soc. 330 (1992), no. 1, 361–370. MR 1094556 (92g:57024), DOI 10.2307/2154169
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- M. Bestvina and M. Handel, Train-tracks for surface homeomorphisms, Topology 34 (1995), no. 1, 109–140. MR 1308491 (96d:57014), DOI 10.1016/0040-9383(94)E0009-9
- Joan S. Birman, Braids, links, and mapping class groups, Princeton University Press, Princeton, N.J., 1974. Annals of Mathematics Studies, No. 82. MR 0375281 (51 \#11477)
- Joan S. Birman and Mark E. Kidwell, Fixed points of pseudo-Anosov diffeomorphisms of surfaces, Adv. in Math. 46 (1982), no. 2, 217–220. MR 679909 (84b:58090), DOI 10.1016/0001-8708(82)90024-X
- Joan S. Birman, Alex Lubotzky, and John McCarthy, Abelian and solvable subgroups of the mapping class groups, Duke Math. J. 50 (1983), no. 4, 1107–1120. MR 726319 (85k:20126), DOI 10.1215/S0012-7094-83-05046-9
- Francis Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988), no. 1, 139–162. MR 931208 (90a:32025), DOI 10.1007/BF01393996
- Philip Boyland, Notes on dynamics of surface homeomorphisms, Warwick, preprint.
- Peter Brinkmann, An implementation of the Bestvina-Handel algorithm for surface homeomorphisms, Experiment. Math. 9 (2000), no. 2, 235–240. MR 1780208 (2001e:57017)
- Peter Brinkmann, A note on pseudo-Anosov maps with small growth rate, Experiment. Math. 13 (2004), no. 1, 49–53. MR 2065567 (2005b:37075)
- John Cantwell and Lawrence Conlon, Handel–Miller theory and finite depth foliations, arXiv:1006.4525.
- Andrew J. Casson and Steven A. Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Mathematical Society Student Texts, vol. 9, Cambridge University Press, Cambridge, 1988. MR 964685 (89k:57025)
- Jin-Hwan Cho and Ji-Young Ham, The minimal dilatation of a genus-two surface, Experiment. Math. 17 (2008), no. 3, 257–267. MR 2455699 (2009i:37096)
- François Dahmani, Vincent Guirardel, and Denis Osin, Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces, arXiv:1111.7048v3.
- André de Carvalho, Toby Hall, and Rupert Venzke, On period minimal pseudo-Anosov braids, Proc. Amer. Math. Soc. 137 (2009), no. 5, 1771–1776. MR 2470836 (2009m:37119), DOI 10.1090/S0002-9939-08-09709-8
- Benson Farb (editor), Problems on mapping class groups and related topics, Proceedings of Symposia in Pure Mathematics, vol. 74, American Mathematical Society, Providence, RI, 2006. MR 2251041 (2007e:57001)
- Benson Farb, Some problems on mapping class groups and moduli space, Problems on mapping class groups and related topics, Proc. Sympos. Pure Math., vol. 74, Amer. Math. Soc., Providence, RI, 2006, pp. 11–55. MR 2264130 (2007h:57018)
- Benson Farb, Christopher J. Leininger, and Dan Margalit, The lower central series and pseudo-Anosov dilatations, Amer. J. Math. 130 (2008), no. 3, 799–827. MR 2418928 (2009d:37072), DOI 10.1353/ajm.0.0005
- Benson Farb, Christopher J. Leininger, and Dan Margalit, Small dilatation pseudo-Anosov homeomorphisms and 3-manifolds, Adv. Math. 228 (2011), no. 3, 1466–1502. MR 2824561 (2012f:37093), DOI 10.1016/j.aim.2011.06.020
- Benson Farb and Dan Margalit, A primer on mapping class groups, Princeton Mathematical Series, vol. 49, Princeton University Press, Princeton, NJ, 2012. MR 2850125 (2012h:57032)
- Albert Fathi, Démonstration d’un théorème de Penner sur la composition des twists de Dehn, Bull. Soc. Math. France 120 (1992), no. 4, 467–484 (French, with English and French summaries). MR 1194272 (93j:57005)
- Sérgio R. Fenley, End periodic surface homeomorphisms and $3$-manifolds, Math. Z. 224 (1997), no. 1, 1–24. MR 1427700 (97m:57023), DOI 10.1007/PL00004576
- John Franks and Michael Handel, Periodic points of Hamiltonian surface diffeomorphisms, Geom. Topol. 7 (2003), 713–756 (electronic). MR 2026545 (2004j:37101), DOI 10.2140/gt.2003.7.713
- David Fried, Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helv. 57 (1982), no. 2, 237–259. MR 684116 (84g:58083), DOI 10.1007/BF02565860
- David Fried, Growth rate of surface homeomorphisms and flow equivalence, Ergodic Theory Dynam. Systems 5 (1985), no. 4, 539–563. MR 829857 (88f:58118), DOI 10.1017/S0143385700003151
- Koji Fujiwara, Subgroups generated by two pseudo-Anosov elements in a mapping class group. II. Uniform bound on exponents, arXiv:0908.0995.
- Jean-Marc Gambaudo, Sebastian van Strien, and Charles Tresser, Vers un ordre de Sarkovskiĭ pour les plongements du disque préservant l’orientation, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 5, 291–294 (French, with English summary). MR 1042866 (91f:58072)
- Marlies Gerber and Anatole Katok, Smooth models of Thurston’s pseudo-Anosov maps, Ann. Sci. École Norm. Sup. (4) 15 (1982), no. 1, 173–204. MR 672479 (84e:58056)
- Ji-Young Ham and Won Taek Song, The minimum dilatation of pseudo-Anosov 5-braids, Experiment. Math. 16 (2007), no. 2, 167–179. MR 2339273 (2008e:37043)
- Michael Handel, Global shadowing of pseudo-Anosov homeomorphisms, Ergodic Theory Dynam. Systems 5 (1985), no. 3, 373–377. MR 805836 (87e:58172), DOI 10.1017/S0143385700003011
- Michael Handel, The forcing partial order on the three times punctured disk, Ergodic Theory Dynam. Systems 17 (1997), no. 3, 593–610. MR 1452182 (98i:57026), DOI 10.1017/S0143385797084940
- Michael Handel and Richard Miller, Handel–Miller theory and finite depth foliations, unpublished.
- Michael Handel and William P. Thurston, New proofs of some results of Nielsen, Adv. in Math. 56 (1985), no. 2, 173–191. MR 788938 (87e:57015), DOI 10.1016/0001-8708(85)90028-3
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- Eriko Hironaka, Small dilatation mapping classes coming from the simplest hyperbolic braid, Algebr. Geom. Topol. 10 (2010), no. 4, 2041–2060. MR 2728483 (2012e:57033), DOI 10.2140/agt.2010.10.2041
- Eriko Hironaka and Eiko Kin, A family of pseudo-Anosov braids with small dilatation, Algebr. Geom. Topol. 6 (2006), 699–738 (electronic). MR 2240913 (2008h:57027), DOI 10.2140/agt.2006.6.699
- Nikolai V. Ivanov, Nielsen numbers of mappings of surfaces, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 122 (1982), 56–65, 163–164 (Russian, with English summary). Studies in topology, IV. MR 661465 (83h:55001)
- Nikolai V. Ivanov, Coefficients of expansion of pseudo-Anosov homeomorphisms, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 167 (1988), no. Issled. Topol. 6, 111–116, 191. MR 964259 (89i:32047)
- Nikolai V. Ivanov, Subgroups of Teichmüller modular groups, Translations of Mathematical Monographs, vol. 115, American Mathematical Society, Providence, RI, 1992. Translated from the Russian by E. J. F. Primrose and revised by the author. MR 1195787 (93k:57031)
- Nikolai V. Ivanov, Mapping class groups, Handbook of geometric topology, North-Holland, Amsterdam, 2002, pp. 523–633. MR 1886678 (2003h:57022)
- Nikolai V. Ivanov, Fifteen problems about the mapping class groups, Problems on mapping class groups and related topics, Proc. Sympos. Pure Math., vol. 74, Amer. Math. Soc., Providence, RI, 2006, pp. 71–80. MR 2264532 (2008b:57003)
- B. Kolev, Periodic orbits of period $3$ in the disc, Nonlinearity 7 (1994), no. 3, 1067–1071. MR 1275541 (95b:58120)
- Irwin Kra, On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981), no. 3-4, 231–270. MR 611385 (82m:32019), DOI 10.1007/BF02392465
- Erwan Lanneau and Jean-Luc Thiffeault, On the minimum dilatation of braids on punctured discs, Geom. Dedicata 152 (2011), 165–182. Supplementary material available online. MR 2795241 (2012h:57035), DOI 10.1007/s10711-010-9551-2
- Erwan Lanneau and Jean-Luc Thiffeault, On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 1, 105–144 (English, with English and French summaries). MR 2828128 (2012e:37070), DOI 10.5802/aif.2599
- Christopher J. Leininger, On groups generated by two positive multi-twists: Teichmüller curves and Lehmer’s number, Geom. Topol. 8 (2004), 1301–1359 (electronic). MR 2119298 (2005j:57002), DOI 10.2140/gt.2004.8.1301
- Darren D. Long and Ulrich Oertel, Hyperbolic surface bundles over the circle, Progress in knot theory and related topics, Travaux en Cours, vol. 56, Hermann, Paris, 1997, pp. 121–142. MR 1603150 (98m:57022)
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Review Information:
Reviewer:
Dan Margalit
Affiliation:
School of Mathematics, Georgia Institute of Technology
Journal:
Bull. Amer. Math. Soc.
51 (2014), 151-161
DOI:
https://doi.org/10.1090/S0273-0979-2013-01419-8
Published electronically:
June 10, 2013
Review copyright:
© Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.