Vanishing and non-vanishing for the first Lp-cohomology of groups

Commentarii Mathematici Helvetici

Volumn 80, Issue 2, 2005, Pages 377-389

  Bourdon, Marc ^a   Martin, Florian ^b   Valette, Alain ^b  

^a UNIV LILLE   (France)

^b UNIVERSITY OF NEUCHÂTEL   (Switzerland)

Author keywords

CAT( 1) space; Critical exponent; Group cohomology; Lp cohomology

Indexed keywords

EID: 27844503471     PISSN: 00102571     EISSN: None     Source Type: Journal    
DOI: 10.4171/CMH/18     Document Type: Article

References (19)

1. [BCG99] G. Besson, G. Courtois, and S. Gallot, Lemme de Schwarz réel et applications géométriques. Acta Math. 183 (1999), 145-169. Zbl 1035.53038 MR 1738042
2. [BH99] M. Bridson and A. Haefliger, Metric spaces of non-positive curvature. Grundlehren Math. Wiss. 319, Springer-Verlag, Berlin 1999. Zbl 0988.53001 MR 1744486
3. [BM96] M. Burger and S. Mozes, CAT(-1) spaces, divergence groups and their commensurators. J. Amer. Math. Soc. 1 (1996), 57-93. Zbl 0847.22004 MR 1325797
4. [Bou95] M. Bourdon, Structure conforme au bord et flot géodésique d'un CAT(-1)-espace. Enseign. Math. 41 (1995), 63-102. Zbl 0871.58069 MR 1341941
5. [Bou96] M. Bourdon, Sur le birapport au bord des CAT(-1)-espaces. Inst. Hautes Études Sci. Publ. Math. 83 (1996), 95-104. Zbl 0883.53047 MR 1423021
6. 2-Betti number. Potential Anal 6 (1997), 313-326. Zbl 0882.22013 MR 1452785
7. 2-cohomology and group cohomology. Topology 25 (1986), 189-215. Zbl 0597.57020 MR 0837621
8. p-cohomology and the conformal dimension of hyperbolic cones. Geom. Dedicata 68 (1997), 263-279. Zbl 0899.53035 MR 1486435
9. [Eym72] P. Eymard, Moyennes invariantes et représentations unitaires. Lecture Notes in Math. 300, Springer-Verlag, Berlin 1972. Zbl 0249.43004 MR 0447969
10. 2 de relations d'équivalence et de groupes. Inst. Hautes Études Sci. Publ. Math. 95 (2002), 93-150. Zbl 1022.37002 MR 1953191
11. [Gro93] M. Gromov, Asymptotic invariants of infinite groups. In Geometric group theory (G. A. Niblo and M. A. Roller, eds.), London Math. Soc. Lecture Notes Ser. 182, Cambridge University Press, Cambridge 1993. Zbl 0841.20039 MR 1253544
12. [Gui72] A. Guichardet, Sur la cohomologie des groupes topologiques II. Bull. Sci. Math. 96 (1972), 305-332. Zbl 0243.57024 MR 0340464
13. [Gui80] A. Guichardet, Cohomologie des groupes topologiques et des algèbres de Lie. Textes Mathématiques, CEDIC/Fernand Nathan, Paris 1980. Zbl 0464.22001 MR 0644979
14. 2-Betti numbers of mapping tori and groups. Topology 33 (1994), 203-214. Zbl 0847.55004 MR 1273782
15. 2-invariants. Math. Ann. 309 (1997), 247-285. Zbl 0886.57028 MR 1474192
16. p des variétés à courbure négative, cas du degré 1. In Partial Differential Equations and Geometry (Torino, 1988), Rend. Sem. Mat. Univ. Politec. Torino, Fase. Spec. 1989, 95-120. Zbl 0723.53023 MR 1086210
17. p-cohomology of finitely generated groups. Canad. Math. Bull. 46 (2003), 268-276. Zbl 1030.43001 MR 1981681
18. [Sha00] Y. Shalom, Rigidity, unitary representations of semisimple groups, and fundamental groups of manifolds with rank one transformation group. Ann. Math. 152 (2000), 113-182. Zbl 0970.22011 MR 1792293
19. [Yue96] C. Yue, Dimension and rigidity of quasi-Fuchsian representations. Ann. of Math. 143 (1996), 331-355. Zbl 0843.22019 MR 1381989