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Projective deformations of weakly orderable hyperbolic Coxeter orbifolds

Suhyoung Choi and Gye-Seon Lee

Geometry & Topology 19 (2015) 1777–1828
Bibliography
1 S Ballas, Deformations of noncompact, projective manifolds, arXiv:1210.8419
2 D Barnette, A proof of the lower bound conjecture for convex polytopes, Pacific J. Math. 46 (1973) 349 MR0328773
3 Y Benoist, Automorphismes des cônes convexes, Invent. Math. 141 (2000) 149 MR1767272
4 Y Benoist, Convexes divisibles, C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 387 MR1826621
5 Y Benoist, Convexes divisibles, III, Ann. Sci. École Norm. Sup. 38 (2005) 793 MR2195260
6 Y Benoist, Convexes hyperboliques et quasiisométries, Geom. Dedicata 122 (2006) 109 MR2295544
7 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. (ALM) 6, International Press (2008) 1 MR2464391
8 Y Benoist, Five lectures on lattices in semisimple Lie groups, from: "Géométries à courbure négative ou nulle, groupes discrets et rigidités" (editors L Bessières, A Parreau, B Rémy), Sémin. Congr. 18, Soc. Math. France (2009) 117 MR2655311
9 J P Benzécri, Sur les variétés localement affines et localement projectives, Bull. Soc. Math. France 88 (1960) 229 MR0124005
10 N Bourbaki, Lie groups and Lie algebras, Chapters 4–6, Elements of Math., Springer (2002) MR1890629
11 A Brøndsted, An introduction to convex polytopes, Graduate Texts in Math. 90, Springer (1983) MR683612
12 R Charney, M Davis, When is a Coxeter system determined by its Coxeter group?, J. London Math. Soc. 61 (2000) 441 MR1760693
13 S Choi, Convex decompositions of real projective surfaces, I: $\pi$–annuli and convexity, J. Differential Geom. 40 (1994) 165 MR1285533
14 S Choi, Convex decompositions of real projective surfaces, II: Admissible decompositions, J. Differential Geom. 40 (1994) 239 MR1293655
15 S Choi, The convex and concave decomposition of manifolds with real projective structures, Mém. Soc. Math. Fr. 78, Soc. Math. France (1999) MR1779499
16 S Choi, Geometric structures on orbifolds and holonomy representations, Geom. Dedicata 104 (2004) 161 MR2043960
17 S Choi, The deformation spaces of projective structures on $3$–dimensional Coxeter orbifolds, Geom. Dedicata 119 (2006) 69 MR2247648
18 S Choi, Geometric structures on $2$–orbifolds: Exploration of discrete symmetry, Math. Soc. Japan Memoirs 27, Math. Soc. Japan (2012) MR2962023
19 S Choi, W M Goldman, The classification of real projective structures on compact surfaces, Bull. Amer. Math. Soc. 34 (1997) 161 MR1414974
20 S Choi, C D Hodgson, G S Lee, Projective deformations of hyperbolic Coxeter $3$–orbifolds, Geom. Dedicata 159 (2012) 125 MR2944525
21 D Cooper, K Delp, The marked length spectrum of a projective manifold or orbifold, Proc. Amer. Math. Soc. 138 (2010) 3361 MR2653965
22 D Cooper, D D Long, M B Thistlethwaite, Computing varieties of representations of hyperbolic $3$–manifolds into $\mathrm{SL}(4,\mathbb{R})$, Experiment. Math. 15 (2006) 291 MR2264468
23 D Cooper, D D Long, M B Thistlethwaite, Flexing closed hyperbolic manifolds, Geom. Topol. 11 (2007) 2413 MR2372851
24 M W Davis, The geometry and topology of Coxeter groups, London Math. Soc. Monographs 32, Princeton Univ. Press (2008) MR2360474
25 M W Davis, Lectures on orbifolds and reflection groups, from: "Transformation groups and moduli spaces of curves" (editors L Ji, S T Yau), Adv. Lect. Math. (ALM) 16, International Press (2011) 63 MR2883685
26 M W Davis, When are two Coxeter orbifolds diffeomorphic?, Michigan Math. J. 63 (2014) 401 MR3215556
27 F Esselmann, The classification of compact hyperbolic Coxeter $d$–polytopes with $d+2$ facets, Comment. Math. Helv. 71 (1996) 229 MR1396674
28 J L Fouquet, H Thuillier, On removable edges in $3$–connected cubic graphs, Discrete Math. 312 (2012) 2652 MR2935416
29 F R Gantmacher, The theory of matrices, Vol. $1$, $2$, Chelsea Publ. (1959) MR0107649
30 W M Goldman, The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984) 200 MR762512
31 W M Goldman, Convex real projective structures on compact surfaces, J. Differential Geom. 31 (1990) 791 MR1053346
32 R Greene, The deformation theory of discrete reflection groups and projective structures, PhD thesis, Ohio State University (2013)
33 B Grünbaum, Convex polytopes, Graduate Texts in Math. 221, Springer (2003) MR1976856
34 M Heusener, J Porti, Infinitesimal projective rigidity under Dehn filling, Geom. Topol. 15 (2011) 2017 MR2860986
35 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
36 V G Kac, È B Vinberg, Quasihomogeneous cones, Mat. Zametki 1 (1967) 347 MR0208470
37 M Kapovich, Deformations of representations of discrete subgroups of $\mathrm{SO}(3,1)$, Math. Ann. 299 (1994) 341 MR1275772
38 J L Koszul, Déformations de connexions localement plates, Ann. Inst. Fourier (Grenoble) 18 (1968) 103 MR0239529
39 N H Kuiper, On convex locally-projective spaces, from: "Convegno Internazionale di Geometria Differenziale, Italia, 1953", Edizioni Cremonese (1954) 200 MR0063115
40 L Marquis, Espace des modules de certains polyèdres projectifs miroirs, Geom. Dedicata 147 (2010) 47 MR2660566
41 D Qi, On irreducible, infinite, nonaffine Coxeter groups, Fund. Math. 193 (2007) 79 MR2284573
42 M S Raghunathan, Discrete subgroups of Lie groups, Springer (1972) MR0507234
43 R K W Roeder, J H Hubbard, W D Dunbar, Andreev's theorem on hyperbolic polyhedra, Ann. Inst. Fourier (Grenoble) 57 (2007) 825 MR2336832
44 W P Thurston, The geometry and topology of three-manifolds, Princeton Univ. Math. Dept. lecture notes (1979)
45 W P Thurston, Three-dimensional geometry and topology, Vol. $1$, Princeton Math. Series 35, Princeton Univ. Press (1997) MR1435975
46 W T Tutte, The factorization of linear graphs, J. London Math. Soc. 22 (1947) 107 MR0023048
47 È B Vinberg, Discrete linear groups that are generated by reflections, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971) 1072 MR0302779
48 È B Vinberg, Hyperbolic groups of reflections, Uspekhi Mat. Nauk 40 (1985) 29, 255 MR783604
49 A Weil, On discrete subgroups of Lie groups, II, Ann. of Math. 75 (1962) 578 MR0137793
50 A Weil, Remarks on the cohomology of groups, Ann. of Math. 80 (1964) 149 MR0169956
51 M Wiemeler, Exotic torus manifolds and equivariant smooth structures on quasitoric manifolds, Math. Z. 273 (2013) 1063 MR3030690