The shape of hyperbolic Dehn surgery space

Geometry and Topology

Volumn 12, Issue 2, 2008, Pages 1033-1090

  Hodgson, Craig ^a   Kerckhoff, Steven ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Harmonic deformation; Hyperbolic Dehn surgery

Indexed keywords

EID: 74249097470     PISSN: 13640380     EISSN: 13640380     Source Type: Journal    
DOI: 10.2140/gt.2008.12.1033     Document Type: Article

References (16)

1. M Atiyah, Elliptic boundary value problems, Annals of Math. Studies 57, Princeton University Press (1965) MR 0198494 Zbl 0137.17002
2. S Boyer, X Zhang, On CullerShalen seminorms and Dehn filling, Ann. of Math. (2) 148 (1998) 737-801 MR 1670053 Zbl 1007.57016
3. J F Brock, K W Bromberg, On the density of geometrically finite Kleinian groups, Acta Math. 192 (2004) 33-93 MR 2079598 Zbl 1055.57020
4. K Bromberg, Hyperbolic conemanifolds, short geodesics, and Schwarzian derivatives, J. Amer. Math. Soc. 17 (2004) 783-826 MR 2083468 Zbl 1061.30037
5. K Bromberg, Projective structures with degenerate holonomy and the Bers density conjecture, Ann. of Math. (2) 166 (2007) 77-93 MR 2342691 Zbl 05241959
6. D Cooper, M Culler, H Gillet, D D Long, P B Shalen, Plane curves associated to character varieties of 3manifolds, Invent. Math. 118 (1994) 47-84 MR 1288467 Zbl 0842.57013
7. M Culler, P B Shalen, Varieties of group representations and splittings of 3manifolds, Ann. of Math. (2) 117 (1983) 109-146 MR 683804 Zbl 0529.57005
8. C D Hodgson, Degeneration and regeneration of geometric structures on 3-manifolds, PhD thesis, Princeton University (1986)
9. C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic conemanifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1-59 MR 1622600 Zbl 0919.57009
10. C D Hodgson, S P Kerckhoff, Harmonic deformations of hyperbolic 3manifolds, from: Kleinian groups and hyperbolic 3 manifolds (Warwick, 2001), London Math. Soc. Lecture Note Ser. 299, Cambridge Univ. Press (2003) 41-73 MR 2044544 Zbl 1051.57018
11. C D Hodgson, S P Kerckhoff, Universal bounds for hyperbolic Dehn surgery, Ann. of Math. (2) 162 (2005) 367-421 MR 2178964 Zbl 1087.57011
12. L Hörmander, Linear partial differential operators, Springer Verlag (1976) MR 0404822 Zbl 0321.35001
13. W D Neumann, D Zagier, Volumes of hyperbolic three manifolds, Topology 24 (1985) 307-332 MR 815482 Zbl 0589.57015
14. J Purcell, Cusp shapes under cone deformation arXiv:math/0410233v3
15. M Spivak, A comprehensive introduction to differential geometry. Vol. III, Publish or Perish (1979) MR 532832 Zbl 0439.53003
16. W Thurston, The geometry and topology of three manifolds (1979)