Smith theory, \(L^2\)-cohomology, isometries of locally symmetric manifolds, and moduli spaces of curves

DOI10.1215/00127094-2382340zbMath1287.57032arXiv1106.1704OpenAlexW3106236286MaRDI QIDQ2443214

Grigori Avramidi

Publication date: 4 April 2014

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.1704

Mathematics Subject Classification ID

Differential geometry of symmetric spaces (53C35) Noncompact Lie groups of transformations (57S20)

Related Items (3)

Periodic flats and group actions on locally symmetric spaces ⋮ One-loop effective action: nonlocal form factors and renormalization group ⋮ Rational manifold models for duality groups

Cites Work

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• The intrinsic asymmetry and inhomogeneity of Teichmüller space
• \(L_ 2\)-cohomology and group cohomology
• The equivariant triangulation theorem for actions of compact Lie groups
• On isometries between Teichmüller spaces
• Approximating \(L^ 2\)-invariants by their finite-dimensional analogues
• Proper actions of lattices on contractible manifolds
• Bounds on the von Neumann dimension of \(L^ 2\)-cohomoloy and the Gauss- Bonnet theorem for open manifolds
• \(L^2\)-invariants of locally symmetric spaces
• The group of isometries of a Finsler space.
• The moduli space of Riemann surfaces is Kähler hyperbolic
• Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
• Isometries, rigidity and universal covers
• Measure homology and singular homology are isometrically isomorphic
• Curve complexes and finite index subgroups of mapping class groups
• Kähler hyperbolicity and \(L_ 2\)-Hodge theory
• The group of isometries of a Riemannian manifold
• Periodic maximal flats are not peripheral
• Degree theorems and Lipschitz simplicial volume for nonpositively curved manifolds of finite volume
• The L^2-cohomology of negatively curved Riemannian symmetric spaces
• On the Residual Finiteness of Certain Mapping Class Groups
• Discrete Subgroups Isomorphic to Lattices in Lie Groups
• The Nielsen realization problem

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