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Trees of Hyperbolic Spaces
About this Title
Michael Kapovich, University of California, Davis, CA and Pranab Sardar, Indian Institute of Science Education and Research, Mohali, India
Publication: Mathematical Surveys and Monographs
Publication Year:
2024; Volume 282
ISBNs: 978-1-4704-7425-6 (print); 978-1-4704-7778-3 (online)
DOI: https://doi.org/10.1090/surv/282
Table of Contents
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Front/Back Matter
Chapters
- Preliminaries on metric geometry
- Graphs of groups and trees of metric spaces
- Carpets, ladders, flow-spaces, metric bundles, and their retractions
- Hyperbolicity of ladders
- Hyperbolicity of flow-spaces
- Hyperbolicity of trees of spaces: Putting everything together
- Description of geodesics
- Cannon–Thurston maps
- Cannon–Thurston maps for elatively hyperbolic spaces
- J. M. Alonso, T. Brady, D. Cooper, V. Ferlini, M. Lustig, M. Mihalik, M. Shapiro, and H. Short, Notes on word hyperbolic groups, Group theory from a geometrical viewpoint (Trieste, 1990) World Sci. Publ., River Edge, NJ, 1991, pp. 3–63. Edited by Short. MR 1170363
- Emina Alibegović, A combination theorem for relatively hyperbolic groups, Bull. London Math. Soc. 37 (2005), no. 3, 459–466. MR 2131400, DOI 10.1112/S0024609304004059
- Hyman Bass, Covering theory for graphs of groups, J. Pure Appl. Algebra 89 (1993), no. 1-2, 3–47. MR 1239551, DOI 10.1016/0022-4049(93)90085-8
- Dmitri Burago, Yuri Burago, and Sergei Ivanov, A course in metric geometry, Graduate Studies in Mathematics, vol. 33, American Mathematical Society, Providence, RI, 2001. MR 1835418, DOI 10.1090/gsm/033
- 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
- M. Bestvina and M. Feighn, A combination theorem for negatively curved groups, J. Differential Geom. 35 (1992), no. 1, 85–101. MR 1152226
- Mladen Bestvina and Mark Feighn, Addendum and correction to: “A combination theorem for negatively curved groups” [J. Differential Geom. 35 (1992), no. 1, 85–101; MR1152226 (93d:53053)], J. Differential Geom. 43 (1996), no. 4, 783–788. MR 1412684
- M. Bestvina, M. Feighn, and M. Handel, Laminations, trees, and irreducible automorphisms of free groups, Geom. Funct. Anal. 7 (1997), no. 2, 215–244. MR 1445386, DOI 10.1007/PL00001618
- Martin R. Bridson and André Haefliger, Metric spaces of non-positive curvature, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999. MR 1744486, DOI 10.1007/978-3-662-12494-9
- Francis Bonahon, Bouts des variétés hyperboliques de dimension $3$, Ann. of Math. (2) 124 (1986), no. 1, 71–158 (French). MR 847953, DOI 10.2307/1971388
- B. H. Bowditch, Geometrical finiteness with variable negative curvature, Duke Math. J. 77 (1995), no. 1, 229–274. MR 1317633, DOI 10.1215/S0012-7094-95-07709-6
- B. H. Bowditch, Convergence groups and configuration spaces, Geometric group theory down under (Canberra, 1996) de Gruyter, Berlin, 1999, pp. 23–54. MR 1714838
- Brian H. Bowditch, Tight geodesics in the curve complex, Invent. Math. 171 (2008), no. 2, 281–300. MR 2367021, DOI 10.1007/s00222-007-0081-y
- B. H. Bowditch, Relatively hyperbolic groups, Internat. J. Algebra Comput. 22 (2012), no. 3, 1250016, 66. MR 2922380, DOI 10.1142/S0218196712500166
- B. H. Bowditch, Stacks of hyperbolic spaces and ends of 3-manifolds, Geometry and topology down under, Contemp. Math., vol. 597, Amer. Math. Soc., Providence, RI, 2013, pp. 65–138. MR 3186670, DOI 10.1090/conm/597/11769
- Brian H. Bowditch, Uniform hyperbolicity of the curve graphs, Pacific J. Math. 269 (2014), no. 2, 269–280. MR 3238474, DOI 10.2140/pjm.2014.269.269
- O. Baker and T. R. Riley, Cannon-Thurston maps do not always exist, Forum Math. Sigma 1 (2013), Paper No. e3, 11. MR 3143716, DOI 10.1017/fms.2013.4
- Owen Baker and Timothy Riley, Cannon-Thurston maps, subgroup distortion, and hyperbolic hydra, Groups Geom. Dyn. 14 (2020), no. 1, 255–282. MR 4077662, DOI 10.4171/ggd/543
- P. Brinkmann, Hyperbolic automorphisms of free groups, Geom. Funct. Anal. 10 (2000), no. 5, 1071–1089. MR 1800064, DOI 10.1007/PL00001647
- M. Bonk and O. Schramm, Embeddings of Gromov hyperbolic spaces, Geom. Funct. Anal. 10 (2000), no. 2, 266–306. MR 1771428, DOI 10.1007/s000390050009
- Inna Bumagin, On definitions of relatively hyperbolic groups, Geometric methods in group theory, Contemp. Math., vol. 372, Amer. Math. Soc., Providence, RI, 2005, pp. 189–196. MR 2139687, DOI 10.1090/conm/372/06884
- 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
- M. Coornaert, T. Delzant, and A. Papadopoulos, Géométrie et théorie des groupes, Lecture Notes in Mathematics, vol. 1441, Springer-Verlag, Berlin, 1990 (French). Les groupes hyperboliques de Gromov. [Gromov hyperbolic groups]; With an English summary. MR 1075994
- Christopher H. Cashen and Alexandre Martin, Quasi-isometries between groups with two-ended splittings, Math. Proc. Cambridge Philos. Soc. 162 (2017), no. 2, 249–291. MR 3604915, DOI 10.1017/S0305004116000530
- James W. Cannon and William P. Thurston, Group invariant Peano curves, Geom. Topol. 11 (2007), 1315–1355. MR 2326947, DOI 10.2140/gt.2007.11.1315
- François Dahmani, Combination of convergence groups, Geom. Topol. 7 (2003), 933–963. MR 2026551, DOI 10.2140/gt.2003.7.933
- Spencer Dowdall, Matthew G. Durham, Christopher J. Leininger, and Alessandro Sisto, Extensions of Veech groups I: A hyperbolic action, J. Topol. 16 (2023), no. 2, 757–805. MR 4637976, DOI 10.1112/topo.12296
- Cornelia Druţu and Michael Kapovich, Geometric group theory, American Mathematical Society Colloquium Publications, vol. 63, American Mathematical Society, Providence, RI, 2018. With an appendix by Bogdan Nica. MR 3753580, DOI 10.1090/coll/063
- Spencer Dowdall, Ilya Kapovich, and Samuel J. Taylor, Cannon-Thurston maps for hyperbolic free group extensions, Israel J. Math. 216 (2016), no. 2, 753–797. MR 3557464, DOI 10.1007/s11856-016-1426-2
- François Dahmani and Mahan Mj, Height, graded relative hyperbolicity and quasiconvexity, J. Éc. polytech. Math. 4 (2017), 515–556 (English, with English and French summaries). MR 3646028, DOI 10.5802/jep.50
- Cornelia Druţu and Mark Sapir, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005), no. 5, 959–1058. With an appendix by Denis Osin and Mark Sapir. MR 2153979, DOI 10.1016/j.top.2005.03.003
- Spencer Dowdall and Samuel J. Taylor, Hyperbolic extensions of free groups, Geom. Topol. 22 (2018), no. 1, 517–570. MR 3720349, DOI 10.2140/gt.2018.22.517
- B. Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998), no. 5, 810–840. MR 1650094, DOI 10.1007/s000390050075
- Michael Freedman, Joel Hass, and Peter Scott, Least area incompressible surfaces in $3$-manifolds, Invent. Math. 71 (1983), no. 3, 609–642. MR 695910, DOI 10.1007/BF02095997
- François Gautero, Hyperbolicity of mapping-torus groups and spaces, Enseign. Math. (2) 49 (2003), no. 3-4, 263–305. MR 2026897
- François Gautero, Geodesics in trees of hyperbolic and relatively hyperbolic spaces, Proc. Edinb. Math. Soc. (2) 59 (2016), no. 3, 701–740. MR 3572767, DOI 10.1017/S0013091515000450
- Étienne Ghys and Pierre de la Harpe, La propriété de Markov pour les groupes hyperboliques, Sur les groupes hyperboliques d’après Mikhael Gromov (Bern, 1988) Progr. Math., vol. 83, Birkhäuser Boston, Boston, MA, 1990, pp. 165–187 (French). MR 1086657, DOI 10.1007/978-1-4684-9167-8_{9}
- S. M. Gersten, Subgroups of word hyperbolic groups in dimension $2$, J. London Math. Soc. (2) 54 (1996), no. 2, 261–283. MR 1405055, DOI 10.1112/jlms/54.2.261
- S. M. Gersten, Cohomological lower bounds for isoperimetric functions on groups, Topology 37 (1998), no. 5, 1031–1072. MR 1650363, DOI 10.1016/S0040-9383(97)00070-0
- Victor Gerasimov, Expansive convergence groups are relatively hyperbolic, Geom. Funct. Anal. 19 (2009), no. 1, 137–169. MR 2507221, DOI 10.1007/s00039-009-0718-7
- François Guéritaud, Olivier Guichard, Fanny Kassel, and Anna Wienhard, Anosov representations and proper actions, Geom. Topol. 21 (2017), no. 1, 485–584. MR 3608719, DOI 10.2140/gt.2017.21.485
- François Gautero and Martin Lustig, Relative hyperbolization of (one-ended hyperbolic)-by-cyclic groups, Math. Proc. Cambridge Philos. Soc. 137 (2004), no. 3, 595–611. MR 2103918, DOI 10.1017/S0305004104007881
- François Gautero, Combinatorial mapping-torus, branched surfaces and free group automorphisms, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), no. 3, 405–440. MR 2370267
- Rita Gitik, Mahan Mitra, Eliyahu Rips, and Michah Sageev, Widths of subgroups, Trans. Amer. Math. Soc. 350 (1998), no. 1, 321–329. MR 1389776, DOI 10.1090/S0002-9947-98-01792-9
- Victor Gerasimov and Leonid Potyagailo, Non-finitely generated relatively hyperbolic groups and Floyd quasiconvexity, Groups Geom. Dyn. 9 (2015), no. 2, 369–434. MR 3356972, DOI 10.4171/GGD/317
- Victor Gerasimov and Leonid Potyagailo, Similar relatively hyperbolic actions of a group, Int. Math. Res. Not. IMRN 7 (2016), 2068–2103. MR 3509947, DOI 10.1093/imrn/rnv170
- M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, DOI 10.1007/978-1-4613-9586-7_{3}
- M. Gromov, Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991) London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295. MR 1253544
- Sébastien Gouëzel and Vladimir Shchur, Corrigendum: A corrected quantitative version of the Morse lemma [ MR3003738], J. Funct. Anal. 277 (2019), no. 4, 1258–1268. MR 3959731, DOI 10.1016/j.jfa.2019.02.021
- O. Guichard. Déformation de sous-groupes discrets de groupes de rang un. PhD thesis, Université Paris 7, 2004.
- Olivier Guichard and Anna Wienhard, Anosov representations: domains of discontinuity and applications, Invent. Math. 190 (2012), no. 2, 357–438. MR 2981818, DOI 10.1007/s00222-012-0382-7
- U. Hamenstädt. Word hyperbolic extension of surface groups. Preprint, arXiv:math/0505244, 2005.
- Allen Hatcher, Algebraic topology, Cambridge University Press, Cambridge, 2002. MR 1867354
- John Hempel, 3-manifolds, AMS Chelsea Publishing, Providence, RI, 2004. Reprint of the 1976 original. MR 2098385, DOI 10.1090/chel/349
- B. Healy and G. C. Hruska. Cusped spaces and quasi-isometries of relatively hyperbolic groups. Arxiv, arXiv:2010.09876, 2020.
- G. Christopher Hruska, Relative hyperbolicity and relative quasiconvexity for countable groups, Algebr. Geom. Topol. 10 (2010), no. 3, 1807–1856. MR 2684983, DOI 10.2140/agt.2010.10.1807
- Woojin Jeon, Ilya Kapovich, Christopher Leininger, and Ken’ichi Ohshika, Conical limit points and the Cannon-Thurston map, Conform. Geom. Dyn. 20 (2016), 58–80. MR 3488025, DOI 10.1090/ecgd/294
- Ilya Kapovich, The combination theorem and quasiconvexity, Internat. J. Algebra Comput. 11 (2001), no. 2, 185–216. MR 1829050, DOI 10.1142/S0218196701000553
- Michael Kapovich, Hyperbolic manifolds and discrete groups, Modern Birkhäuser Classics, Birkhäuser Boston, Ltd., Boston, MA, 2009. Reprint of the 2001 edition. MR 2553578, DOI 10.1007/978-0-8176-4913-5
- M. Kapovich. A note on properly discontinuous actions. San Paulo Journal of Math Sciences, 2023. \PrintDOI{10.1007/s40863-023-00353-z}.
- Michael Kapovich and Bernhard Leeb, Discrete isometry groups of symmetric spaces, Handbook of group actions. Vol. IV, Adv. Lect. Math. (ALM), vol. 41, Int. Press, Somerville, MA, 2018, pp. 191–290. MR 3888689
- Michael Kapovich and Bernhard Leeb, Finsler bordifications of symmetric and certain locally symmetric spaces, Geom. Topol. 22 (2018), no. 5, 2533–2646. MR 3811766, DOI 10.2140/gt.2018.22.2533
- Michael Kapovich and Beibei Liu, Geometric finiteness in negatively pinched Hadamard manifolds, Ann. Acad. Sci. Fenn. Math. 44 (2019), no. 2, 841–875. MR 3973544, DOI 10.5186/aasfm.2019.4444
- Erica Klarreich, Semiconjugacies between Kleinian group actions on the Riemann sphere, Amer. J. Math. 121 (1999), no. 5, 1031–1078. MR 1713300
- Erica Klarreich, The boundary at infinity of the curve complex and the relative Teichmüller space, Groups Geom. Dyn. 16 (2022), no. 2, 705–723. MR 4502619, DOI 10.4171/ggd/662
- Michael Kapovich, Bernhard Leeb, and Joan Porti, Anosov subgroups: dynamical and geometric characterizations, Eur. J. Math. 3 (2017), no. 4, 808–898. MR 3736790, DOI 10.1007/s40879-017-0192-y
- O. Kharlampovich and A. Myasnikov, Hyperbolic groups and free constructions, Trans. Amer. Math. Soc. 350 (1998), no. 2, 571–613. MR 1390041, DOI 10.1090/S0002-9947-98-01773-5
- Mahan Mj and Pranab Sardar, A combination theorem for metric bundles, Geom. Funct. Anal. 22 (2012), no. 6, 1636–1707. MR 3000500, DOI 10.1007/s00039-012-0196-1
- Jason Fox Manning, Geometry of pseudocharacters, Geom. Topol. 9 (2005), 1147–1185. MR 2174263, DOI 10.2140/gt.2005.9.1147
- Yair N. Minsky, On rigidity, limit sets, and end invariants of hyperbolic $3$-manifolds, J. Amer. Math. Soc. 7 (1994), no. 3, 539–588. MR 1257060, DOI 10.1090/S0894-0347-1994-1257060-3
- Yair N. Minsky, Combinatorial and geometrical aspects of hyperbolic 3-manifolds, Kleinian groups and hyperbolic 3-manifolds (Warwick, 2001) London Math. Soc. Lecture Note Ser., vol. 299, Cambridge Univ. Press, Cambridge, 2003, pp. 3–40. MR 2044543, DOI 10.1017/CBO9780511542817.002
- Yair N. Minsky, End invariants and the classification of hyperbolic 3-manifolds, Current developments in mathematics, 2002, Int. Press, Somerville, MA, 2003, pp. 181–217. MR 2062319
- M. Mitra, Ending laminations for hyperbolic group extensions, Geom. Funct. Anal. 7 (1997), no. 2, 379–402. MR 1445392, DOI 10.1007/PL00001624
- Mahan Mitra, Cannon-Thurston maps for trees of hyperbolic metric spaces, J. Differential Geom. 48 (1998), no. 1, 135–164. MR 1622603
- Mahan Mitra, On a theorem of Scott and Swarup, Proc. Amer. Math. Soc. 127 (1999), no. 6, 1625–1631. MR 1610757, DOI 10.1090/S0002-9939-99-04935-7
- Mahan Mitra, Height in splittings of hyperbolic groups, Proc. Indian Acad. Sci. Math. Sci. 114 (2004), no. 1, 39–54. MR 2040599, DOI 10.1007/BF02829670
- Mahan Mj, Cannon-Thurston maps for surface groups, Ann. of Math. (2) 179 (2014), no. 1, 1–80. MR 3126566, DOI 10.4007/annals.2014.179.1.1
- Mahan Mj, Ending laminations and Cannon-Thurston maps, Geom. Funct. Anal. 24 (2014), no. 1, 297–321. With an appendix by Shubhabrata Das and Mj. MR 3177384, DOI 10.1007/s00039-014-0263-x
- Mahan Mj, Cannon-Thurston maps for surface groups: an exposition of amalgamation geometry and split geometry, Geometry, topology, and dynamics in negative curvature, London Math. Soc. Lecture Note Ser., vol. 425, Cambridge Univ. Press, Cambridge, 2016, pp. 221–271. MR 3497262
- Mahan Mj, Cannon-Thurston maps for Kleinian groups, Forum Math. Pi 5 (2017), e1, 49. MR 3652816, DOI 10.1017/fmp.2017.2
- D. McCullough, A. Miller, and G. A. Swarup, Uniqueness of cores of noncompact $3$-manifolds, J. London Math. Soc. (2) 32 (1985), no. 3, 548–556. MR 825931, DOI 10.1112/jlms/s2-32.3.548
- Harold Marston Morse, A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Amer. Math. Soc. 26 (1924), no. 1, 25–60. MR 1501263, DOI 10.1090/S0002-9947-1924-1501263-9
- Lee Mosher, A hyperbolic-by-hyperbolic hyperbolic group, Proc. Amer. Math. Soc. 125 (1997), no. 12, 3447–3455. MR 1443845, DOI 10.1090/S0002-9939-97-04249-4
- Mahan Mj and Abhijit Pal, Relative hyperbolicity, trees of spaces and Cannon-Thurston maps, Geom. Dedicata 151 (2011), 59–78. MR 2780738, DOI 10.1007/s10711-010-9519-2
- Mahan Mj and Lawrence Reeves, A combination theorem for strong relative hyperbolicity, Geom. Topol. 12 (2008), no. 3, 1777–1798. MR 2421140, DOI 10.2140/gt.2008.12.1777
- Mahan Mj and Kasra Rafi, Algebraic ending laminations and quasiconvexity, Algebr. Geom. Topol. 18 (2018), no. 4, 1883–1916. MR 3797060, DOI 10.2140/agt.2018.18.1883
- Mahan Mj and Pranab Sardar, A combination theorem for metric bundles, Geom. Funct. Anal. 22 (2012), no. 6, 1636–1707. MR 3000500, DOI 10.1007/s00039-012-0196-1
- Howard Masur and Saul Schleimer, The geometry of the disk complex, J. Amer. Math. Soc. 26 (2013), no. 1, 1–62. MR 2983005, DOI 10.1090/S0894-0347-2012-00742-5
- John M. Mackay and Alessandro Sisto, Maps between relatively hyperbolic spaces and between their boundaries, Trans. Amer. Math. Soc. 377 (2024), no. 2, 1409–1454. MR 4688555, DOI 10.1090/tran/9063
- Jean Pierre Mutanguha, The dynamics and geometry of free group endomorphisms, Adv. Math. 384 (2021), Paper No. 107714, 60. MR 4237417, DOI 10.1016/j.aim.2021.107714
- Ken’ichi Ohshika, Constructing geometrically infinite groups on boundaries of deformation spaces, J. Math. Soc. Japan 61 (2009), no. 4, 1261–1291. MR 2588511
- Denis V. Osin, Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems, Mem. Amer. Math. Soc. 179 (2006), no. 843, vi+100. MR 2182268, DOI 10.1090/memo/0843
- Jean-Pierre Otal, The hyperbolization theorem for fibered 3-manifolds, SMF/AMS Texts and Monographs, vol. 7, American Mathematical Society, Providence, RI; Société Mathématique de France, Paris, 2001. Translated from the 1996 French original by Leslie D. Kay. MR 1855976
- Abhijit Pal and Akshay Kumar Singh, Relatively hyperbolic spaces, Geometry, groups and dynamics, Contemp. Math., vol. 639, Amer. Math. Soc., Providence, RI, 2015, pp. 307–325. MR 3379836, DOI 10.1090/conm/639/12792
- John Roe, Lectures on coarse geometry, University Lecture Series, vol. 31, American Mathematical Society, Providence, RI, 2003. MR 2007488, DOI 10.1090/ulect/031
- E. Rips and Z. Sela, Structure and rigidity in hyperbolic groups. I, Geom. Funct. Anal. 4 (1994), no. 3, 337–371. MR 1274119, DOI 10.1007/BF01896245
- Pranab Sardar, Graphs of hyperbolic groups and a limit set intersection theorem, Proc. Amer. Math. Soc. 146 (2018), no. 5, 1859–1871. MR 3767341, DOI 10.1090/proc/13871
- G. P. Scott, Finitely generated $3$-manifold groups are finitely presented, J. London Math. Soc. (2) 6 (1973), 437–440. MR 380763, DOI 10.1112/jlms/s2-6.3.437
- G. P. Scott, Compact submanifolds of $3$-manifolds, J. London Math. Soc. (2) 7 (1973), 246–250. MR 326737, DOI 10.1112/jlms/s2-7.2.246
- Z. Sela, Acylindrical accessibility for groups, Invent. Math. 129 (1997), no. 3, 527–565. MR 1465334, DOI 10.1007/s002220050172
- Jean-Pierre Serre, Trees, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003. Translated from the French original by John Stillwell; Corrected 2nd printing of the 1980 English translation. MR 1954121
- Hamish Short, Quasiconvexity and a theorem of Howson’s, Group theory from a geometrical viewpoint (Trieste, 1990) World Sci. Publ., River Edge, NJ, 1991, pp. 168–176. MR 1170365
- Alessandro Sisto, Projections and relative hyperbolicity, Enseign. Math. (2) 59 (2013), no. 1-2, 165–181. MR 3113603, DOI 10.4171/LEM/59-1-6
- Peter Scott and Terry Wall, Topological methods in group theory, Homological group theory (Proc. Sympos., Durham, 1977) London Math. Soc. Lecture Note Ser., vol. 36, Cambridge Univ. Press, Cambridge-New York, 1979, pp. 137–203. MR 564422
- Eric L. Swenson, Quasi-convex groups of isometries of negatively curved spaces, Topology Appl. 110 (2001), no. 1, 119–129. Geometric topology and geometric group theory (Milwaukee, WI, 1997). MR 1804703, DOI 10.1016/S0166-8641(99)00166-2
- W. P. Thurston. The Geometry and Topology of 3-Manifolds. Princeton University Notes, 1980.
- Pekka Tukia, Conical limit points and uniform convergence groups, J. Reine Angew. Math. 501 (1998), 71–98. MR 1637829, DOI 10.1515/crll.1998.081
- Jussi Väisälä, Gromov hyperbolic spaces, Expo. Math. 23 (2005), no. 3, 187–231. MR 2164775, DOI 10.1016/j.exmath.2005.01.010