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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Systole et rayon interne des variétés hyperboliques non compactes

Matthieu Gendulphe

Geometry & Topology 19 (2015) 2039–2080
Bibliography
1 C C Adams, The noncompact hyperbolic $3$–manifold of minimal volume, Proc. Amer. Math. Soc. 100 (1987) 601 MR894423
2 C C Adams, Volumes of $N$–cusped hyperbolic $3$–manifolds, J. London Math. Soc. 38 (1988) 555 MR972138
3 C C Adams, Waist size for cusps in hyperbolic $3$–manifolds, Topology 41 (2002) 257 MR1876890
4 C C Adams, Hyperbolic knots, from: "Handbook of knot theory" (editors W Menasco, M Thistlethwaite), Elsevier (2005) 1 MR2179259
5 C C Adams, A W Reid, Systoles of hyperbolic $3$–manifolds, Math. Proc. Cambridge Philos. Soc. 128 (2000) 103 MR1724432
6 I Agol, Systoles of hyperbolic $4$–manifolds, arXiv:math/0612290
7 R Bacher, A Vdovina, Counting $1$–vertex triangulations of oriented surfaces, Discrete Math. 246 (2002) 13 MR1884884
8 C Bavard, La systole des surfaces hyperelliptiques, prépublication de l’ENS Lyon (1992)
9 C Bavard, Disques extrémaux et surfaces modulaires, Ann. Fac. Sci. Toulouse Math. 5 (1996) 191 MR1413853
10 C Bavard, Systole et invariant d'Hermite, J. Reine Angew. Math. 482 (1997) 93 MR1427658
11 M V Belolipetsky, S A Thomson, Systoles of hyperbolic manifolds, Algebr. Geom. Topol. 11 (2011) 1455 MR2821431
12 N Bergeron, F Haglund, D T Wise, Hyperplane sections in arithmetic hyperbolic manifolds, J. Lond. Math. Soc. 83 (2011) 431 MR2776645
13 F Bonahon, J P Otal, Variétés hyperboliques à géodésiques arbitrairement courtes, Bull. London Math. Soc. 20 (1988) 255 MR931188
14 K Böröczky, Packing of spheres in spaces of constant curvature, Acta Math. Acad. Sci. Hungar. 32 (1978) 243 MR512399
15 P Buser, H Karcher, Gromov's almost flat manifolds, Astérisque 81, Soc. Math. France (1981) 148 MR619537
16 P Buser, P Sarnak, On the period matrix of a Riemann surface of large genus, Invent. Math. 117 (1994) 27 MR1269424
17 J DeBlois, The centered dual and the maximal injectivity radius of hyperbolic surfaces, Geom. Topol. 19 (2015) 953 MR3336276
18 W Feit, Orders of finite linear groups, from: "Proceedings of the First Jamaican Conference on Group Theory and its Applications" (editors T Foguel, J Minty), Univ. West Indies (1996) 9 MR1484185
19 S Friedland, Discrete groups of unitary isometries and balls in hyperbolic manifolds, from: "Proceedings of the Fourth Conference of the International Linear Algebra Society" (editors H Bart, L F Elsner, A C M Ran), Linear Algebra Appl. 241/243 (1996) 305 MR1400448
20 S Friedland, The maximal orders of finite subgroups in $\mathrm{GL}_n(\mathbf{Q})$, Proc. Amer. Math. Soc. 125 (1997) 3519 MR1443385
21 S Friedland, S Hersonsky, Jorgensen's inequality for discrete groups in normed algebras, Duke Math. J. 69 (1993) 593 MR1208812
22 D Gabai, R Meyerhoff, P Milley, Minimum volume cusped hyperbolic three-manifolds, J. Amer. Math. Soc. 22 (2009) 1157 MR2525782
23 M Gendulphe, Paysage systolique des surfaces hyperboliques de caractéristique $-1$, prépublication arXiv:math/0508036
24 H Gieseking, Analytische Untersuchungen über topologische Gruppen, PhD thesis, Münster (1912)
25 E Girondo, G González-Diez, On extremal discs inside compact hyperbolic surfaces, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 57 MR1703263
26 M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1 MR697984
27 M Gromov, Systoles and intersystolic inequalities, from: "Actes de la Table Ronde de Géométrie Différentielle" (editor A L Besse), Sémin. Congr. 1, Soc. Math. France (1996) 291 MR1427763
28 L Guth, Notes on Gromov's systolic estimate, Geom. Dedicata 123 (2006) 113 MR2299729
29 L Guth, Metaphors in systolic geometry, from: "Proceedings of the International Congress of Mathematicians, Vo II" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan), Hindustan Book Agency (2010) 745 MR2827817
30 U Haagerup, H J Munkholm, Simplices of maximal volume in hyperbolic $n$–space, Acta Math. 147 (1981) 1 MR631085
31 S Hersonsky, Covolume estimates for discrete groups of hyperbolic isometries having parabolic elements, Michigan Math. J. 40 (1993) 467 MR1236173
32 C D Hodgson, J R Weeks, Symmetries, isometries and length spectra of closed hyperbolic three-manifolds, Experiment. Math. 3 (1994) 261 MR1341719
33 F Jenni, Über den ersten Eigenwert des Laplace-Operators auf ausgewählten Beispielen kompakter Riemannscher Flächen, Comment. Math. Helv. 59 (1984) 193 MR749104
34 R Kellerhals, Ball packings in spaces of constant curvature and the simplicial density function, J. Reine Angew. Math. 494 (1998) 189 MR1604407
35 R Kellerhals, Volumes of cusped hyperbolic manifolds, Topology 37 (1998) 719 MR1607720
36 R Kellerhals, Collars in $\mathrm{PSL}(2,\mathbf{H})$, Ann. Acad. Sci. Fenn. Math. 26 (2001) 51 MR1816562
37 R Kellerhals, Quaternions and some global properties of hyperbolic $5$–manifolds, Canad. J. Math. 55 (2003) 1080 MR2005283
38 R Kellerhals, On the structure of hyperbolic manifolds, Israel J. Math. 143 (2004) 361 MR2106991
39 G S Lakeland, C J Leininger, Systoles and Dehn surgery for hyperbolic 3-manifolds, Algebr. Geom. Topol. 14 (2014) 1441 MR3190600
40 W Magnus, Residually finite groups, Bull. Amer. Math. Soc. 75 (1969) 305 MR0241525
41 A Marden, Outer circles, Cambridge Univ. Press (2007) MR2355387
42 T H Marshall, Asymptotic volume formulae and hyperbolic ball packing, Ann. Acad. Sci. Fenn. Math. 24 (1999) 31 MR1677993
43 G J Martin, Balls in hyperbolic manifolds, J. London Math. Soc. 40 (1989) 257 MR1044273
44 J Martinet, Perfect lattices in Euclidean spaces, Grundl. Math. Wissen. 327, Springer (2003) MR1957723
45 R Meyerhoff, Sphere-packing and volume in hyperbolic $3$–space, Comment. Math. Helv. 61 (1986) 271 MR856090
46 J Milnor, Collected papers, Vol. 1: Geometry, Publish or Perish (1994) MR1277810
47 W Plesken, M Pohst, On maximal finite irreducible subgroups of $\mathrm{GL}(n, \mathbf{Z})$, V: The eight-dimensional case and a complete description of dimensions less than ten, Math. Comp. 34 (1980) 277 MR551305
48 A Przeworski, Cones embedded in hyperbolic manifolds, J. Differential Geom. 58 (2001) 219 MR1913942
49 J S Purcell, J Souto, Geometric limits of knot complements, J. Topol. 3 (2010) 759 MR2746337
50 A Reznikov, The volume and the injectivity radius of a hyperbolic manifold, Topology 34 (1995) 477 MR1318888
51 C A Rogers, The packing of equal spheres, Proc. London Math. Soc. 8 (1958) 609 MR0102052
52 P Schmutz, Riemann surfaces with shortest geodesic of maximal length, Geom. Funct. Anal. 3 (1993) 564 MR1250756
53 P Schmutz, Congruence subgroups and maximal Riemann surfaces, J. Geom. Anal. 4 (1994) 207 MR1277506
54 W P Thurston, The geometry and topology of three-manifolds, lecture notes, Princeton University (1978)
55 M Wada, Conjugacy invariants of Möbius transformations, Complex Variables Theory Appl. 15 (1990) 125 MR1058518
56 P L Waterman, An inscribed ball for Kleinian groups, Bull. London Math. Soc. 16 (1984) 525 MR751826
57 J R Weeks, SnapPea
58 A Yamada, On Marden's universal constant of Fuchsian groups, II, J. Analyse Math. 41 (1982) 234 MR687954