On the Betti numbers of a hyperbolic manifold

DOI10.1007/BF01895709zbMath0777.11019MaRDI QIDQ1190130

Xiaoxi Xue

Publication date: 27 September 1992

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/58142

zbMATH Keywords

hyperbolic manifoldlower boundscohomology of arithmetic groupsarithmetic latticenonvanishing results for Betti numbers

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Cohomology of arithmetic groups (11F75)

Related Items

On 2-systoles of hyperbolic 3-manifolds ⋮ Regular simplices and lower volume bounds for hyperbolic \(n\)-manifolds ⋮ Hyperbolic manifolds with a large number of systoles ⋮ The density hypothesis for horizontal families of lattices ⋮ A tower of coverings of quasi-projective varieties ⋮ Geometric cycles, arithmetic groups and their cohomology ⋮ Asymptotics of Betti numbers of arithmetic varieties ⋮ Betti numbers on a tower of coverings

Cites Work

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• Geometric construction of cohomology for arithmetic groups. I
• Some applications of the Weil representation
• On the first Betti numbers of hyperbolic surfaces
• On Matsushima's formula for the Betti numbers of a locally symmetric space
• On the first Betti number of a constant negatively curved manifold
• Betti numbers of congruence groups. (Appendix: On representations of compact \(p\)-adic groups by Ze'ev Rudnick)
• On the first Betti number of compact quotient spaces of higher-dimensional symmetric spaces
• Non-vanishing theorems for the cohomology of certain arithmetic quotients.