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Hyperbolic Dehn filling in dimension four

Bruno Martelli and Stefano Riolo

Geometry & Topology 22 (2018) 1647–1716
Bibliography
1 D V Alekseevskij, È B Vinberg, A S Solodovnikov, Geometry of spaces of constant curvature, from: "Geometry, II", Encyclopaedia Math. Sci. 29, Springer (1993) 1 MR1254932
2 E M Andreev, The intersection of the planes of the faces of polyhedra with sharp angles, Mat. Zametki 8 (1970) 521 MR0279680
3 M Boileau, B Leeb, J Porti, Geometrization of 3–dimensional orbifolds, Ann. of Math. 162 (2005) 195 MR2178962
4 K Bromberg, Hyperbolic cone-manifolds, short geodesics, and Schwarzian derivatives, J. Amer. Math. Soc. 17 (2004) 783 MR2083468
5 D Cooper, C D Hodgson, S P Kerckhoff, Three-dimensional orbifolds and cone-manifolds, 5, Mathematical Society of Japan (2000) MR1778789
6 D A Derevnin, A D Mednykh, M G Pashkevich, The volume of a symmetric tetrahedron in a hyperbolic and a spherical space, Sibirsk. Mat. Zh. 45 (2004) 1022 MR2108500
7 K Fujiwara, J F Manning, CAT(0) and CAT(1) fillings of hyperbolic manifolds, J. Differential Geom. 85 (2010) 229 MR2732977
8 K Fujiwara, J F Manning, Simplicial volume and fillings of hyperbolic manifolds, Algebr. Geom. Topol. 11 (2011) 2237 MR2826938
9 H Garland, M S Raghunathan, Fundamental domains for lattices in (–)rank 1 semisimple Lie groups, Ann. of Math. 92 (1970) 279 MR0267041
10 R Guglielmetti, M Jacquemet, R Kellerhals, Commensurability of hyperbolic Coxeter groups: theory and computation, preprint (2017)
11 C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1 MR1622600
12 M Jacquemet, New contributions to hyperbolic polyhedra, reflection groups, and their commensurability, PhD thesis, Université de Fribourg (2015)
13 S P Kerckhoff, P A Storm, From the hyperbolic 24–cell to the cuboctahedron, Geom. Topol. 14 (2010) 1383 MR2653730
14 S Kojima, Deformations of hyperbolic 3–cone-manifolds, J. Differential Geom. 49 (1998) 469 MR1669649
15 A Kolpakov, B Martelli, Hyperbolic four-manifolds with one cusp, Geom. Funct. Anal. 23 (2013) 1903 MR3132905
16 C Maclachlan, Commensurability classes of discrete arithmetic hyperbolic groups, Groups Geom. Dyn. 5 (2011) 767 MR2836459
17 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
18 C T McMullen, The Gauss–Bonnet theorem for cone manifolds and volumes of moduli spaces, Amer. J. Math. 139 (2017) 261 MR3619915
19 G Montcouquiol, On the rigidity of hyperbolic cone-manifolds, C. R. Math. Acad. Sci. Paris 340 (2005) 677 MR2139276
20 G Montcouquiol, Déformations Einstein infinitésimales de cones-variétés hyperboliques, preprint (2006) arXiv:math/0603514
21 G D Mostow, Strong rigidity of locally symmetric spaces, 78, Princeton Univ. Press (1973) MR0385004
22 G Prasad, Strong rigidity of –rank 1 lattices, Invent. Math. 21 (1973) 255 MR0385005
23 S Riolo, L Slavich, New hyperbolic 4–manifolds of low volume, preprint (2017) arXiv:1710.07534
24 L Slavich, The complement of the figure-eight knot geometrically bounds, Proc. Amer. Math. Soc. 145 (2017) 1275 MR3589325
25 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
26 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. (1998) 511 MR1668340
27 È B Vinberg, Hyperbolic groups of reflections, Uspekhi Mat. Nauk 40 (1985) 29 MR783604
28 H Weiss, Local rigidity of 3–dimensional cone-manifolds, J. Differential Geom. 71 (2005) 437 MR2198808
29 H Weiss, Global rigidity of 3–dimensional cone-manifolds, J. Differential Geom. 76 (2007) 495 MR2331529