Some Open Problems About Aspherical Closed Manifolds

DOI10.1007/978-3-319-05254-0_3zbMath1327.57001OpenAlexW318772949MaRDI QIDQ2948972

Wolfgang Lück

Publication date: 7 October 2015

Published in: Trends in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-05254-0_3

zbMATH Keywords

rigidityfundamental groupconjecturesuniversal coveringzero-in-the-spectrum conjectureBorel conjecture\(S^1\)-actionsimplicial volumeSinger conjecturePoincaré duality group\(L^2\)-Betti numbershomological growth\(L^2\) torsionaspherical closed manifoldsrandom closed manifoldsRiemannian metric with positive scalar curvature

Mathematics Subject Classification ID

Rigidity results (53C24) Other groups related to topology or analysis (20F38) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) Poincaré duality spaces (57P10) Topological manifolds (57N99) Research exposition (monographs, survey articles) pertaining to (K)-theory (19-02)

Cites Work

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• Property (T) and Kazhdan constants for discrete groups
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• Negatively Curved Manifolds with Exotic Smooth Structures
• ALMOST EVERY GROUP IS HYPERBOLIC
• Isomorphism Conjectures in Algebraic K-Theory
• The asymptotic growth of torsion homology for arithmetic groups
• The Farrell-Jones Conjecture for cocompact lattices in virtually connected Lie groups
• Closed aspherical manifolds with center
• Riemannian geometry
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