Volume 17, issue 1 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Complex twist flows on surface group representations and the local shape of the deformation space of hyperbolic cone–$3$–manifolds

Grégoire Montcouquiol and Hartmut Weiß

Geometry & Topology 17 (2013) 369–412
Bibliography
1 M F Atiyah, R Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983) 523 MR702806
2 M Boileau, B Leeb, J Porti, Geometrization of 3–dimensional orbifolds, Ann. of Math. 162 (2005) 195 MR2178962
3 D Cooper, C D Hodgson, S P Kerckhoff, Three-dimensional orbifolds and cone-manifolds, 5, Mathematical Society of Japan (2000) MR1778789
4 W M Goldman, The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984) 200 MR762512
5 W M Goldman, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math. 85 (1986) 263 MR846929
6 W M Goldman, Geometric structures on manifolds and varieties of representations, from: "Geometry of group representations" (editors W M Goldman, A R Magid), Contemp. Math. 74, Amer. Math. Soc. (1988) 169 MR957518
7 W M Goldman, Topological components of spaces of representations, Invent. Math. 93 (1988) 557 MR952283
8 W M Goldman, The complex-symplectic geometry of SL(2, )–characters over surfaces, from: "Algebraic groups and arithmetic" (editors S G Dani, G Prasad), Tata Inst. Fund. Res. (2004) 375 MR2094117
9 W J Harvey, Boundary structure of the modular group, from: "Riemann surfaces and related topics : Proceedings of the 1978 Stony Brook Conference" (editors I Kra, B Maskit), Ann. of Math. Stud. 97, Princeton Univ. Press (1981) 245 MR624817
10 C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1 MR1622600
11 W P A Klingenberg, Riemannian geometry, 1, Walter de Gruyter & Co. (1995) MR1330918
12 K Krasnov, J M Schlenker, Minimal surfaces and particles in 3–manifolds, Geom. Dedicata 126 (2007) 187 MR2328927
13 F Luo, G Tian, Liouville equation and spherical convex polytopes, Proc. Amer. Math. Soc. 116 (1992) 1119 MR1137227
14 H A Masur, Y N Minsky, Geometry of the complex of curves, I, Hyperbolicity, Invent. Math. 138 (1999) 103 MR1714338
15 R Mazzeo, G Montcouquiol, Infinitesimal rigidity of cone-manifolds and the Stoker problem for hyperbolic and Euclidean polyhedra, J. Differential Geom. 87 (2011) 525 MR2819548
16 R Mazzeo, H Weiss, Teichmüller theory for conic surfaces, in preparation
17 G Montcouquiol, Deformations of hyperbolic convex polyhedra and cone–3–manifolds, to appear in Geom. Dedicata (2013)
18 G D Mostow, Quasi-conformal mappings in n–space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. (1968) 53 MR0236383
19 J Porti, Regenerating hyperbolic cone structures from Nil, Geom. Topol. 6 (2002) 815 MR1943382
20 J Porti, H Weiss, Deforming Euclidean cone 3–manifolds, Geom. Topol. 11 (2007) 1507 MR2326950
21 J M Schlenker, Dihedral angles of convex polyhedra, Discrete Comput. Geom. 23 (2000) 409 MR1744513
22 J J Stoker, Geometrical problems concerning polyhedra in the large, Comm. Pure Appl. Math. 21 (1968) 119 MR0222765
23 W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. Lecture Notes (1979)
24 W P Thurston, Earthquakes in two-dimensional hyperbolic geometry, from: "Low-dimensional topology and Kleinian groups" (editor D B A Epstein), London Math. Soc. Lecture Note Ser. 112, Cambridge Univ. Press (1986) 91 MR903860
25 W P Thurston, Shapes of polyhedra and triangulations of the sphere, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1, Geom. Topol. Publ., Coventry (1998) 511 MR1668340
26 V A Toponogov, Evaluation of the length of a closed geodesic on a convex surface, Dokl. Akad. Nauk SSSR 124 (1959) 282 MR0102055
27 M Troyanov, Prescribing curvature on compact surfaces with conical singularities, Trans. Amer. Math. Soc. 324 (1991) 793 MR1005085
28 A Weil, On discrete subgroups of Lie groups, Ann. of Math. 72 (1960) 369 MR0137792
29 H Weiss, Local rigidity of 3–dimensional cone-manifolds, J. Differential Geom. 71 (2005) 437 MR2198808
30 H Weiss, Global rigidity of 3–dimensional cone-manifolds, J. Differential Geom. 76 (2007) 495 MR2331529
31 H Weiss, The deformation theory of hyperbolic cone-3–manifolds with cone-angles less than 2π, Geom. Topol. 17 (2013) 329