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Book Information:

Author: J. H. Hubbard
Title: Teichmüller theory and applications to geometry, topology, and dynamics. Volume 1: Teichmüller theory
Additional book information: Matrix Editions, Ithaca, NY, 2006, xx+459 pp., ISBN 978-0-9715766-2-9

Author: J. H. Hubbard
Title: Teichmüller theory and applications to geometry, topology, and dynamics. Volume 2: Surface homeomorphisms and rational functions
Additional book information: Matrix Editions, Ithaca, NY, 2016, x+262 pp., ISBN 978-1-943863-00-6

Jayadev Athreya, Alexander Bufetov, Alex Eskin, and Maryam Mirzakhani, Lattice point asymptotics and volume growth on Teichmüller space, Duke Math. J. 161 (2012), no. 6, 1055–1111. MR 2913101, DOI 10.1215/00127094-1548443

Lipman Bers, On boundaries of Teichmüller spaces and on Kleinian groups. I, Ann. of Math. (2) 91 (1970), 570–600. MR 297992, DOI 10.2307/1970638

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

Lipman Bers, On Teichmüller’s proof of Teichmüller’s theorem, J. Analyse Math. 46 (1986), 58–64. MR 861688, DOI 10.1007/BF02796573

Jeffrey F. Brock, The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores, J. Amer. Math. Soc. 16 (2003), no. 3, 495–535. MR 1969203, DOI 10.1090/S0894-0347-03-00424-7

Jeffrey F. Brock, Richard D. Canary, and Yair N. Minsky, The classification of Kleinian surface groups, II: The ending lamination conjecture, Ann. of Math. (2) 176 (2012), no. 1, 1–149. MR 2925381, DOI 10.4007/annals.2012.176.1.1

Adrien Douady and John H. Hubbard, A proof of Thurston’s topological characterization of rational functions, Acta Math. 171 (1993), no. 2, 263–297. MR 1251582, DOI 10.1007/BF02392534

Albert Fathi, François Laudenbach, and Valentin Poénaru, Thurston’s work on surfaces, Mathematical Notes, vol. 48, Princeton University Press, Princeton, NJ, 2012. Translated from the 1979 French original by Djun M. Kim and Dan Margalit. MR 3053012

Jane Gilman, On the Nielsen type and the classification for the mapping class group, Adv. in Math. 40 (1981), no. 1, 68–96. MR 616161, DOI 10.1016/0001-8708(81)90033-5

Jane Gilman, Determining Thurston classes using Nielsen types, Trans. Amer. Math. Soc. 272 (1982), no. 2, 669–675. MR 662059, DOI 10.1090/S0002-9947-1982-0662059-X

A. Grothendieck, Techniques de construction en géométrie analytique, Séminaire Henri Cartan, tome 13 (1960–1961), exposés no. 7 to 17.

Athanase Papadopoulos (ed.), Handbook of Teichmüller theory. Vol. VI, IRMA Lectures in Mathematics and Theoretical Physics, vol. 27, European Mathematical Society (EMS), Zürich, 2016. MR 3560242, DOI 10.4171/160

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

S. Viera Ferreira Levy, Critically finite rational maps, PhD dissertation, Princeton University, 1985.

Curt McMullen, Amenability, Poincaré series and quasiconformal maps, Invent. Math. 97 (1989), no. 1, 95–127. MR 999314, DOI 10.1007/BF01850656

Curt McMullen, Riemann surfaces and the geometrization of $3$-manifolds, Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 2, 207–216. MR 1153266, DOI 10.1090/S0273-0979-1992-00313-0

Curtis T. McMullen, Renormalization and 3-manifolds which fiber over the circle, Annals of Mathematics Studies, vol. 142, Princeton University Press, Princeton, NJ, 1996. MR 1401347, DOI 10.1515/9781400865178

C. McMullen, Iteration on Teichmüller space, Invent. Math. 99 (1990), no. 2, 425–454. MR 1031909, DOI 10.1007/BF01234427

Curt McMullen, Rational maps and Kleinian groups, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991, pp. 889–899. MR 1159274

Curtis T. McMullen and Dennis P. Sullivan, Quasiconformal homeomorphisms and dynamics. III. The Teichmüller space of a holomorphic dynamical system, Adv. Math. 135 (1998), no. 2, 351–395. MR 1620850, DOI 10.1006/aima.1998.1726

Yair Minsky, The classification of Kleinian surface groups. I. Models and bounds, Ann. of Math. (2) 171 (2010), no. 1, 1–107. MR 2630036, DOI 10.4007/annals.2010.171.1

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

Maryam Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math. 167 (2007), no. 1, 179–222. MR 2264808, DOI 10.1007/s00222-006-0013-2

Maryam Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Ann. of Math. (2) 168 (2008), no. 1, 97–125. MR 2415399, DOI 10.4007/annals.2008.168.97

Maryam Mirzakhani, On Weil-Petersson volumes and geometry of random hyperbolic surfaces, Proceedings of the International Congress of Mathematicians. Volume II, Hindustan Book Agency, New Delhi, 2010, pp. 1126–1145. MR 2827834

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, Abbildungsklassen endlicher Ordnung, Acta Math. 75 (1943), 23–115 (German). MR 13306, DOI 10.1007/BF02404101

J. Nielsen, Surface transformation classes of algebraically finite type, Danske Vid. Selsk. Math.-Phys. Medd. 21, (1944). no. 2, 89 pp., in: Collected mathematical papers. Vol. 2, Contemporary Mathematicians. Birkhäuser, Boston MA, 1986, pp. 233–319.

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 and J. L. Harer, Combinatorics of train tracks, Annals of Mathematics Studies, vol. 125, Princeton University Press, Princeton, NJ, 1992. MR 1144770, DOI 10.1515/9781400882458

R. C. Penner, Moduli spaces and macromolecules, Bull. Amer. Math. Soc. (N.S.) 53 (2016), no. 2, 217–268. MR 3474307, DOI 10.1090/bull/1524

Reinhold Remmert, From Riemann surfaces to complex spaces, Matériaux pour l’histoire des mathématiques au XX$^\textrm {e}$ siècle (Nice, 1996) Sémin. Congr., vol. 3, Soc. Math. France, Paris, 1998, pp. 203–241 (English, with English and French summaries). MR 1640261, DOI 10.1007/978-1-4757-2956-6_{9}

B. Riemann, Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse (Göttingen, 1851), Gesammelte mathematische Werke, pp. 3–48.

B. Riemann, Theorie der Abel’schen Functionen, J. Reine Angew. Math. 54 (1857), 115–155 (German). MR 1579035, DOI 10.1515/crll.1857.54.115

Dennis Sullivan, Linking the universalities of Milnor-Thurston, Feigenbaum and Ahlfors-Bers, Topological methods in modern mathematics (Stony Brook, NY, 1991) Publish or Perish, Houston, TX, 1993, pp. 543–564. MR 1215976

Oswald Teichmüller, Extremale quasikonforme Abbildungen und quadratische Differentiale, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1939 (1940), no. 22, 197 (German). MR 0003242

Oswald Teichmüller, Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1943 (1943), no. 4, 42 (German). MR 0017803

Oswald Teichmüller, Variable Riemann surfaces, Handbook of Teichmüller theory. Vol. IV, IRMA Lect. Math. Theor. Phys., vol. 19, Eur. Math. Soc., Zürich, 2014, pp. 787–803. Translated from the German [MR0018762] by Annette A’Campo-Neuen. MR 3289716, DOI 10.4171/117-1/19

William P. Thurston, Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series, vol. 35, Princeton University Press, Princeton, NJ, 1997. Edited by Silvio Levy. MR 1435975

William P. Thurston, On the geometry and dynamics of iterated rational maps, Complex dynamics, A K Peters, Wellesley, MA, 2009, pp. 3–137. Edited by Dierk Schleicher and Nikita Selinger and with an appendix by Schleicher. MR 2508255, DOI 10.1201/b10617-3

W. P. Thurston, The combinatorics of iterated rational maps, lecture notes, 1983 and several later versions.

• Jayadev Athreya, Alexander Bufetov, Alex Eskin, and Maryam Mirzakhani, Lattice point asymptotics and volume growth on Teichmüller space, Duke Math. J. 161 (2012), no. 6, 1055–1111. MR 2913101, DOI 10.1215/00127094-1548443
• Lipman Bers, On boundaries of Teichmüller spaces and on Kleinian groups. I, Ann. of Math. (2) 91 (1970), 570–600. MR 0297992, DOI 10.2307/1970638
• Lipman Bers, An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), no. 1-2, 73–98. MR 0477161, DOI 10.1007/BF02545743
• Lipman Bers, On Teichmüller’s proof of Teichmüller’s theorem, J. Analyse Math. 46 (1986), 58–64. MR 861688, DOI 10.1007/BF02796573
• Jeffrey F. Brock, The Weil-Petersson metric and volumes of $3$-dimensional hyperbolic convex cores, J. Amer. Math. Soc. 16 (2003), no. 3, 495–535. MR 1969203, DOI 10.1090/S0894-0347-03-00424-7
• Jeffrey F. Brock, Richard D. Canary, and Yair N. Minsky, The classification of Kleinian surface groups, II: The ending lamination conjecture, Ann. of Math. (2) 176 (2012), no. 1, 1–149. MR 2925381, DOI 10.4007/annals.2012.176.1.1
• Adrien Douady and John H. Hubbard, A proof of Thurston’s topological characterization of rational functions, Acta Math. 171 (1993), no. 2, 263–297. MR 1251582, DOI 10.1007/BF02392534
• Albert Fathi, François Laudenbach, and Valentin Poénaru, Thurston’s work on surfaces, Mathematical Notes, vol. 48, Princeton University Press, Princeton, NJ, 2012. Translated from the 1979 French original by Djun M. Kim and Dan Margalit. MR 3053012
• Jane Gilman, On the Nielsen type and the classification for the mapping class group, Adv. in Math. 40 (1981), no. 1, 68–96. MR 616161, DOI 10.1016/0001-8708(81)90033-5
• Jane Gilman, Determining Thurston classes using Nielsen types, Trans. Amer. Math. Soc. 272 (1982), no. 2, 669–675. MR 662059, DOI 10.2307/1998720
• A. Grothendieck, Techniques de construction en géométrie analytique, Séminaire Henri Cartan, tome 13 (1960–1961), exposés no. 7 to 17.
• Athanase Papadopoulos (ed.), Handbook of Teichmüller theory. Vol. VI, IRMA Lectures in Mathematics and Theoretical Physics, vol. 27, European Mathematical Society (EMS), Zürich, 2016. MR 3560242, DOI 10.4171/160
• 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
• S. Viera Ferreira Levy, Critically finite rational maps, PhD dissertation, Princeton University, 1985.
• Curt McMullen, Amenability, Poincaré series and quasiconformal maps, Invent. Math. 97 (1989), no. 1, 95–127. MR 999314, DOI 10.1007/BF01850656
• Curt McMullen, Riemann surfaces and the geometrization of $3$-manifolds, Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 2, 207–216. MR 1153266, DOI 10.1090/S0273-0979-1992-00313-0
• Curtis T. McMullen, Renormalization and $3$-manifolds which fiber over the circle, Annals of Mathematics Studies, vol. 142, Princeton University Press, Princeton, NJ, 1996. MR 1401347, DOI 10.1515/9781400865178
• C. McMullen, Iteration on Teichmüller space, Invent. Math. 99 (1990), no. 2, 425–454. MR 1031909, DOI 10.1007/BF01234427
• Curt McMullen, Rational maps and Kleinian groups, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991, pp. 889–899. MR 1159274
• Curtis T. McMullen and Dennis P. Sullivan, Quasiconformal homeomorphisms and dynamics. III. The Teichmüller space of a holomorphic dynamical system, Adv. Math. 135 (1998), no. 2, 351–395. MR 1620850, DOI 10.1006/aima.1998.1726
• Yair Minsky, The classification of Kleinian surface groups. I. Models and bounds, Ann. of Math. (2) 171 (2010), no. 1, 1–107. MR 2630036, DOI 10.4007/annals.2010.171.1
• 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
• Maryam Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math. 167 (2007), no. 1, 179–222. MR 2264808, DOI 10.1007/s00222-006-0013-2
• Maryam Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Ann. of Math. (2) 168 (2008), no. 1, 97–125. MR 2415399, DOI 10.4007/annals.2008.168.97
• Maryam Mirzakhani, On Weil-Petersson volumes and geometry of random hyperbolic surfaces, Proceedings of the International Congress of Mathematicians. Volume II, Hindustan Book Agency, New Delhi, 2010, pp. 1126–1145. MR 2827834
• 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, Abbildungsklassen endlicher Ordnung, Acta Math. 75 (1943), 23–115 (German). MR 0013306, DOI 10.1007/BF02404101
• J. Nielsen, Surface transformation classes of algebraically finite type, Danske Vid. Selsk. Math.-Phys. Medd. 21, (1944). no. 2, 89 pp., in: Collected mathematical papers. Vol. 2, Contemporary Mathematicians. Birkhäuser, Boston MA, 1986, pp. 233–319.
• Robert C. Penner, A construction of pseudo-Anosov homeomorphisms, Trans. Amer. Math. Soc. 310 (1988), no. 1, 179–197. MR 930079, DOI 10.2307/2001116
• R. C. Penner and J. L. Harer, Combinatorics of train tracks, Annals of Mathematics Studies, vol. 125, Princeton University Press, Princeton, NJ, 1992. MR 1144770, DOI 10.1515/9781400882458
• R. C. Penner, Moduli spaces and macromolecules, Bull. Amer. Math. Soc. (N.S.) 53 (2016), no. 2, 217–268. MR 3474307, DOI 10.1090/bull/1524
• Reinhold Remmert, From Riemann surfaces to complex spaces, Matériaux pour l’histoire des mathématiques au XX$^\textrm {e}$ siècle (Nice, 1996) Sémin. Congr., vol. 3, Soc. Math. France, Paris, 1998, pp. 203–241 (English, with English and French summaries). MR 1640261, DOI 10.1007/978-1-4757-2956-6_9
• B. Riemann, Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse (Göttingen, 1851), Gesammelte mathematische Werke, pp. 3–48.
• B. Riemann, Theorie der Abel’schen Functionen, J. Reine Angew. Math. 54 (1857), 115–155 (German). MR 1579035, DOI 10.1515/crll.1857.54.115
• Dennis Sullivan, Linking the universalities of Milnor-Thurston, Feigenbaum and Ahlfors-Bers, Topological methods in modern mathematics (Stony Brook, NY, 1991) Publish or Perish, Houston, TX, 1993, pp. 543–564. MR 1215976
• Oswald Teichmüller, Extremale quasikonforme Abbildungen und quadratische Differentiale, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1939 (1940), no. 22, 197 (German). MR 0003242
• Oswald Teichmüller, Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1943 (1943), no. 4, 42 (German). MR 0017803
• Oswald Teichmüller, Variable Riemann surfaces, Handbook of Teichmüller theory. Vol. IV, IRMA Lect. Math. Theor. Phys., vol. 19, Eur. Math. Soc., Zürich, 2014, pp. 787–803. Translated from the German [MR0018762] by Annette A’Campo-Neuen. MR 3289716, DOI 10.4171/117-1/19
• William P. Thurston, Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series, vol. 35, Princeton University Press, Princeton, NJ, 1997. Edited by Silvio Levy. MR 1435975
• William P. Thurston, On the geometry and dynamics of iterated rational maps, Complex dynamics, A K Peters, Wellesley, MA, 2009, pp. 3–137. Edited by Dierk Schleicher and Nikita Selinger and with an appendix by Schleicher. MR 2508255, DOI 10.1201/b10617-3
• W. P. Thurston, The combinatorics of iterated rational maps, lecture notes, 1983 and several later versions.