@article{TSG_1999-2000__18__17_0, author = {Nicolas Bergeron}, title = {Sur l'homologie et le spectre des vari\'et\'es hyperboliques}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {17--26}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {18}, year = {1999-2000}, doi = {10.5802/tsg.217}, zbl = {0980.58022}, mrnumber = {1812207}, language = {fr}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.217/} }
TY - JOUR AU - Nicolas Bergeron TI - Sur l'homologie et le spectre des variétés hyperboliques JO - Séminaire de théorie spectrale et géométrie PY - 1999-2000 SP - 17 EP - 26 VL - 18 PB - Institut Fourier PP - Grenoble UR - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.217/ DO - 10.5802/tsg.217 LA - fr ID - TSG_1999-2000__18__17_0 ER -
%0 Journal Article %A Nicolas Bergeron %T Sur l'homologie et le spectre des variétés hyperboliques %J Séminaire de théorie spectrale et géométrie %D 1999-2000 %P 17-26 %V 18 %I Institut Fourier %C Grenoble %U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.217/ %R 10.5802/tsg.217 %G fr %F TSG_1999-2000__18__17_0
Nicolas Bergeron. Sur l'homologie et le spectre des variétés hyperboliques. Séminaire de théorie spectrale et géométrie, Volume 18 (1999-2000), pp. 17-26. doi : 10.5802/tsg.217. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.217/
[1] I. R. Aitchison and J. H. Rubinstein, Combinatorial cubings, cusps, and the dodecahedral knots, Topology '90 (Columbus, OH, 1990), 17-26, Ohio State Univ. Math. Res. Inst. Publ., 1, de Gruyter, Berlin, 1992. | MR | Zbl
[2] I. R. Aitchison and J. H. Rubinstein, Geodesic surfaces in knot complements, Experiment Math. 6 ( 1997), n° 2,137-150. | MR | Zbl
[3] M. D. Baker, The virtual ℤ-representability of certain 3-manifold groups, Proc. Amer. Math. Soc. 103 ( 1988), n° 3, 996-998. | MR | Zbl
[4] N. Bergeron, Premier nombre de Betti et spectre du laplacien de certaines variétés hyperboliques, à paraître dans L'Enseignement Mathématique. | Zbl
[5] P. Buser, Geometry and spectra of compact Riemann surfaces, Birkhäuser ( 1992). | MR | Zbl
[6] A. Borei, Compact Clifford-Klein forms of symmetric spaces, Topology 2 ( 1963), 111-122. | MR | Zbl
[7] H. S. M. Coxeter, Regular honeycombs in hyperbolic space, Proceedings of the International Congress of Mathematicians, 1954, Amsterdam, vol. III, pp. 155-169. Erven P. Noordhoff N.V., Groningen; North-Holland Publishing Co., Amsterdam, 1956. | MR | Zbl
[8] M. Gromov and I. Piateski-Shapiro, Non-arithmetic groups in Lobachevsky spaces, Publ. Math. I. H. E. S., pp. 93-103 ( 1988). | Numdam | Zbl
[9] A. Hatcher, Hyperbolic structures of arithmetic type on some link complements, J. London Math. Soc. (2), 27 ( 1983), 345-355. | MR | Zbl
[10] H. Hilden, M. Lozano and J. Montesinos, On knots that are universal, Topology 24 ( 1985), 499-504. | MR | Zbl
[11] S. Kojima and D. D. Long, Virtual Betti numbers of some hyperbolic 3-manifolds, A fête of topology, 417-437, Academic Press, Boston, MA, ( 1988). | MR | Zbl
[12] D. D. Long, Immersions and embeddings of totally geodesic surfaces, Buil. London Math. Soc. 19, pp. 481-484( 1987). | MR | Zbl
[13] A. Lubotzky, Free quotients and the first Betti number of some hyperbolic manifolds, Transform. Groups 1, pp. 71-82 ( 1996). | MR | Zbl
[14] J. G. Ratcliffe, Fondations of hyperbolic manifolds, Graduate Texts in Mathematics 149, Springer-Verlag ( 1994). | MR | Zbl
[15] A. W. Reid, Totally geodesic surfaces in hyperbolic 3-manifotds, Proc. Edimburgh Math. Soc. ( 1991) 34, 77-88. | MR | Zbl
[16] A. W. Reid, Isospectrality and commensurability of arithmetic hyperbolic 2- and 3-manifolds, Duke Math. J. ( 1992) 65, 215-228. | MR | Zbl
[17] P. Scott, Subgroups of surface groups are aimost geometric, J. London Math. Soc. 17 (2) ( 1978) 555-565. | MR | Zbl
[18] A. Selberg, On discontinuous groups in higher-dimensional symmetric spaces, in: Contributions to Function Theory, edited by K. Chandrasekharan, Tata Inst. of Fund. Research, Bombay ( 1960), 147-164. | MR | Zbl
[19] R. J. Spatzier, On isospectral locally symmetric spaces and a theorem of von Neumann, Duke Math. J. ( 1989) 59, 289-294; Correction, Duke Math. J. ( 1990) 60, 561. | MR | Zbl
[20] M.-F. Vignéras, Variétés Riemanniennes isospectrales et non isométriques, Ann. of Math. ( 1980) 112, 21-32. | MR | Zbl
[21] E. B. Vinberg, Geometry II, Encyclopedia of Mathematical Sciences, 29, Springer-Verlag ( 1993). | MR | Zbl
Cited by Sources: