Cannon-Thurston maps for pared manifolds of bounded geometry

Geometry and Topology

Volumn 13, Issue 1, 2009, Pages 189-245

  Mj, Mahan ^a  

^a RAMAKRISHNA MISSION VIVEKANANDA UNIVERSITY   (India)

Author keywords

Cannon thurston maps; Local connectivity of limit sets

Indexed keywords

EID: 74249115501     PISSN: 13640380     EISSN: 13640380     Source Type: Journal    
DOI: 10.2140/gt.2009.13.189     Document Type: Article

References (49)

1. W Abikoff, Kleinian groups-geometrically finite and geometrically perverse, from: Geometry of group representations (Boulder, CO, 1987), Contemp. Math. 74, Amer. Math. Soc. (1988) 1-50 MR957510
2. J W Anderson, B Maskit, On the local connectivity of limit set of Kleinian groups, Complex Variables Theory Appl. 31 (1996) 177-183 MR1423249
3. M Bestvina, Geometric group theory problem list (2004)
4. M Bestvina, M Feighn, A combination theorem for negatively curved groups, J. Differential Geom. 35 (1992) 85-101 MR1152226
5. M Bestvina, M Feighn, M Handel, Laminations, trees, and irreducible automorphisms of free groups, Geom. Funct. Anal. 7 (1997) 215-244 MR1445386
6. M Bestvina, M Handel, Train tracks and automorphisms of free groups, Ann. Of Math. (2) 135 (1992) 1-51 MR1147956
7. F Bonahon, Bouts des variétés hyperboliques de dimension 3, Ann. of Math. (2) 124 (1986) 71-158 MR847953
8. B H Bowditch, Relatively hyperbolic groups, preprint, Southampton (1997)
9. B H Bowditch, A topological characterisation of hyperbolic groups, J. Amer. Math. Soc. 11 (1998) 643-667 MR1602069
10. B H Bowditch, Convergence groups and configuration spaces, from: Geometric group theory down under (Canberra, 1996) (editors J. Cossey, C. Miller, W. Neumann and M. Shapiro), de Gruyter (1999) 23-54 MR1714838
11. B H Bowditch, Stacks of hyperbolic spaces and ends of 3 manifolds, preprint, Southampton (2002)
12. B H Bowditch, The Cannon-Thurston map for puncturedsurface groups, Math. Z. 255 (2007) 35-76 MR2262721
13. J F Brock, Iteration of mapping classes and limits of hyperbolic 3-manifolds, Invent. Math. 143 (2001) 523-570 MR1817644
14. J F Brock, R D Canary, Y N Minsky, The Classification of Kleinian surface groups II: The Ending Lamination Conjecture, preprint (2004)
15. J W Cannon, W P Thurston, Group invariant Peano curves, Geom. Topol. 11 (2007) 1315-1355 MR2326947
16. M Coornaert, T Delzant, A Papadopoulos, Géométrie et théorie des groupes, Lecture Notes in Mathematics 1441, Springer (1990) MR1075994 Les groupes hyperboliques de Gromov. iGromov hyperbolic groups], With an English summary
17. B Farb, Relatively hyperbolic groups, Geom. Funct. Anal. 8 (1998) 810-840 MR1650094
18. W J Floyd, Group completions and limit sets of Kleinian groups, Invent. Math. 57 (1980) 205-218 MR568933
19. Sur les groupes hyperboliques d'après Mikhael Gromov (editors É. Ghys and P. Harpe), Progress in Mathematics 83, Birkhäuser (1990) MR1086648 Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988
20. M Gromov, Hyperbolic groups, from: Essays in group theory, Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75-263 MR919829
21. M Gromov, Metric structures for Riemannian and nonRiemannian spaces, Progress in Mathematics 152, Birkhäuser (1999) MR1699320 Based on the 1981 French original
22. J G Hocking, G S Young, Topology, Addison-Wesley Publishing Co., Reading, MALondon (1961) MR0125557
23. E Klarreich, Semiconjugacies between Kleinian group actions on the Riemann sphere, Amer. J. Math. 121 (1999) 1031-1078 MR1713300
24. C T McMullen, Amenability, Poincaré series and quasiconformal maps, Invent. Math. 97 (1989) 95-127 MR999314
25. C T McMullen, Iteration on Teichmüller space, Invent. Math. 99 (1990) 425-454 MR1031909
26. C T McMullen, Local connectivity, Kleinian groups and geodesics on the blowup of the torus, Invent. Math. 146 (2001) 35-91 MR1859018
27. Y N Minsky, Teichmüller geodesics and ends of hyperbolic 3manifolds, Topology 32 (1993) 625-647 MR1231968
28. Y N Minsky, On rigidity, limit sets, and end invariants of hyperbolic 3-manifolds, J. Amer. Math. Soc. 7 (1994) 539-588 MR1257060
29. Y N Minsky, The classification of puncturedtorus groups, Ann. of Math. (2) 149 (1999) 559-626 MR1689341
30. Y N Minsky, Bounded geometry for Kleinian groups, Invent. Math. 146 (2001) 143-192 MR1859020
31. Y N Minsky, The classification of Kleinian surface groups I: Models and Bounds, preprint (2002)
32. Y N Minsky, End invariants and the classification of hyperbolic 3-manifolds, from: "Current developments in mathematics, 2002", Int. Press, Somerville, MA (2003) 181-217 MR2062319
33. M Mitra, PhD thesis, UC Berkeley (1997)
34. M Mitra, Ending laminations for hyperbolic group extensions, Geom. Funct. Anal. 7 (1997) 379-402 MR1445392
35. M Mitra, Cannon-Thurston maps for hyperbolic group extensions, Topology 37 (1998) 527-538 MR1604882
36. M Mitra, Cannon-Thurston maps for trees of hyperbolic metric spaces, J. Differential Geom. 48 (1998) 135-164 MR1622603
37. H Miyachi, Semiconjugacies between actions of topologically tame Kleinian groups, preprint (2002)
38. M Mj, Cannon-Thurston Maps for Surface Groups I: Amalgamation Geometry and Split Geometry (2005) arXiv:math.GT/0512539
39. M Mj, Cannon-Thurston maps, i-bounded geometry and a theorem of McMullen (2005) arXiv:math.GT/0511041
40. M Mj, Cannon-Thurston Maps for Surface Groups II: Split Geometry and the Minsky Model (2006) arXiv:math.GT0607509
41. M Mj, A Pal, Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps (2007) arXiv:0708.3578
42. R M Myers, From Beowulf to Virginia Woolf: An astounding and wholly unauthorized history of English literature, Bobbs-Merrill, Indianapolis (1952)
43. A Pal, Relative Hyperbolic Extensions of Groups and Cannon-Thurston Maps (2008) arXiv:0801.0933
44. G P Scott, Compact submanifolds of 3-manifolds, J. London Math. Soc. (2) 7 (1973) 246-250 MR0326737
45. J Souto, Cannon-Thurston maps for thick free groups, preprint (2006)
46. W P Thurston, The geometry and topology of 3-manifolds, Princeton University notes (1980)
47. W P Thurston, Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds, Ann. of Math. (2) 124 (1986) 203-246 MR855294
48. W P Thurston, Hyperbolic structures on 3-manifolds. III. Deformation of 3-manifolds with incompressible boundary, preprint (1986)
49. A Yaman, A topological characterisation of relatively hyperbolic groups, J. Reine Angew. Math. 566 (2004) 41-89 MR2039323.