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Convex projective structures on nonhyperbolic three-manifolds

Samuel A Ballas, Jeffrey Danciger and Gye-Seon Lee

Geometry & Topology 22 (2018) 1593–1646
Bibliography
1 Y Benoist, Convexes divisibles, III, Ann. Sci. École Norm. Sup. 38 (2005) 793 MR2195260
2 Y Benoist, Convexes divisibles, IV : Structure du bord en dimension 3, Invent. Math. 164 (2006) 249 MR2218481
3 Y Benoist, Convexes hyperboliques et quasiisométries, Geom. Dedicata 122 (2006) 109 MR2295544
4 Y Benoist, A survey on divisible convex sets, from: "Geometry, analysis and topology of discrete groups" (editors L Ji, K Liu, L Yang, S T Yau), Adv. Lect. Math. 6, International (2008) 1 MR2464391
5 H U Boden, S Friedl, Metabelian SL(N, ) representations of knot groups, III : Deformations, Q. J. Math. 65 (2014) 817 MR3261968
6 B A Burton, R Budney, W Pettersson, others, Regina : software for 3–manifold topology and normal surface theory, (1999–)
7 J O Button, A 3–manifold group which is not four dimensional linear, J. Pure Appl. Algebra 218 (2014) 1604 MR3188859
8 E Calabi, On compact, Riemannian manifolds with constant curvature, I, from: "Differential geometry" (editor C B Allendorfer), Proc. Sympos. Pure Math. 3, Amer. Math. Soc. (1961) 155 MR0133787
9 R D Canary, D B A Epstein, P Green, Notes on notes of Thurston, from: "Analytical and geometric aspects of hyperbolic space" (editor D B A Epstein), London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 3 MR903850
10 S Choi, A classification of radial or totally geodesic ends of real projective orbifolds, I: A survey of results, preprint (2015) arXiv:1501.00348
11 S Choi, The convex real projective orbifolds with radial or totally geodesic ends: a survey of some partial results, from: "In the tradition of Ahlfors–Bers, VII" (editors A S Basmajian, Y N Minsky, A W Reid), Contemp. Math. 696, Amer. Math. Soc. (2017) 51 MR3715441
12 S Choi, G S Lee, L Marquis, Projective deformations of hyperbolic Coxeter 3–orbifolds of finite volume, in preparation
13 D Cooper, D Long, M Thistlethwaite, Computing varieties of representations of hyperbolic 3–manifolds into SL(4, ), Experiment. Math. 15 (2006) 291 MR2264468
14 D Cooper, D D Long, M B Thistlethwaite, Flexing closed hyperbolic manifolds, Geom. Topol. 11 (2007) 2413 MR2372851
15 D Cooper, D Long, S Tillmann, Deforming convex projective manifolds, Geom. Topol. 22 (2018) 1349
16 M Culler, N M Dunfield, J R Weeks, SnapPy : a computer program for studying the topology of 3–manifolds, (2015)
17 J Danciger, A geometric transition from hyperbolic to anti-de Sitter geometry, Geom. Topol. 17 (2013) 3077 MR3190306
18 C Ehresmann, Sur les espaces localement homogenes, Enseign. Math. 35 (1936) 317
19 E Fominykh, S Garoufalidis, M Goerner, V Tarkaev, A Vesnin, A census of tetrahedral hyperbolic manifolds, Exp. Math. 25 (2016) 466 MR3499710
20 W M Goldman, Affine manifolds and projective geometry on surfaces, BA thesis, Princeton University (1977)
21 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
22 W M Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990) 791 MR1053346
23 P de la Harpe, On Hilbert’s metric for simplices, from: "Geometric group theory, I" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 181, Cambridge Univ. Press (1993) 97 MR1238518
24 M Heusener, O Medjerab, Deformations of reducible representations of knot groups into SL(n, ), Math. Slovaca 66 (2016) 1091 MR3602606
25 M Heusener, J Porti, Infinitesimal projective rigidity under Dehn filling, Geom. Topol. 15 (2011) 2017 MR2860986
26 M Heusener, J Porti, E Suárez Peiró, Deformations of reducible representations of 3–manifold groups into SL2(), J. Reine Angew. Math. 530 (2001) 191 MR1807271
27 C D Hodgson, S P Kerckhoff, Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery, J. Differential Geom. 48 (1998) 1 MR1622600
28 D Johnson, J J Millson, Deformation spaces associated to compact hyperbolic manifolds, from: "Discrete groups in geometry and analysis" (editor R Howe), Progr. Math. 67, Birkhäuser (1987) 48 MR900823
29 M Kapovich, Hyperbolic manifolds and discrete groups, 183, Birkhäuser (2001) MR1792613
30 M Kapovich, Convex projective structures on Gromov–Thurston manifolds, Geom. Topol. 11 (2007) 1777 MR2350468
31 J L Koszul, Déformations de connexions localement plates, Ann. Inst. Fourier (Grenoble) 18 (1968) 103 MR0239529
32 L Marquis, Espace des modules de certains polyèdres projectifs miroirs, Geom. Dedicata 147 (2010) 47 MR2660566
33 S Nakajima, Über konvexe Kurven und Flächen, Tôhoku Math. J. 29 (1928) 227
34 P Przytycki, D T Wise, Mixed 3–manifolds are virtually special, J. Amer. Math. Soc. 31 (2018) 319 MR3758147
35 J G Ratcliffe, Foundations of hyperbolic manifolds, 149, Springer (2006) MR2249478
36 R W Richardson, Commuting varieties of semisimple Lie algebras and algebraic groups, Compositio Math. 38 (1979) 311 MR535074
37 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
38 H Tietze, Über Konvexheit im kleinen und im großen und über gewisse den Punkten einer Menge zugeordnete Dimensionszahlen, Math. Z. 28 (1928) 697 MR1544985
39 È B Vinberg, Discrete linear groups that are generated by reflections, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971) 1072 MR0302779
40 A Weil, On discrete subgroups of Lie groups, Ann. of Math. 72 (1960) 369 MR0137792
41 A Weil, On discrete subgroups of Lie groups, II, Ann. of Math. 75 (1962) 578 MR0137793
42 D T Wise, Research announcement: the structure of groups with a quasiconvex hierarchy, Electron. Res. Announc. Math. Sci. 16 (2009) 44 MR2558631
43 D T Wise, The structure of groups with a quasiconvex hierarchy, preprint (2011)