Equivariant Euler characteristics and \(K\)-homology Euler classes for proper cocompact \(G\)-manifolds

DOI10.2140/gt.2003.7.569zbMath1034.19003arXivmath/0208164OpenAlexW3102797026MaRDI QIDQ1426932

Wolfgang Lück, Jonathan M. Rosenberg

Publication date: 15 March 2004

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0208164

zbMATH Keywords

Burnside ringcyclic subgroupssignature operatorKasparov theoryequivariant K-homologyde Rham operatorequivariant Euler characteristicEuler operatorequivariant Euler classfixed setsequivariant Poincaré-Hopf theoremuniversal equivariant Euler characteristic

Mathematics Subject Classification ID

Equivariant algebraic topology of manifolds (57R91) Exotic index theories on manifolds (58J22) Discontinuous groups of transformations (57S30) Ext and (K)-homology (19K33) Kasparov theory ((KK)-theory) (19K35) Equivariant homotopy theory in algebraic topology (55P91) Equivariant (K)-theory (19L47) Index theory (19K56)

Related Items (4)

An orbifold relative index theorem ⋮ Euler characteristics and Gysin sequences for group actions on boundaries ⋮ A Lefschetz fixed-point formula for certain orbifold C*-algebras ⋮ Transversals, duality, and irrational rotation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher \(G\)-signatures for Lipschitz manifolds
• The local structure of tangent G-vector fields
• Transformation groups
• Equivariant SKK and vector field bordism
• Equivariant KK-theory and the Novikov conjecture
• Transformation groups and algebraic \(K\)-theory
• Generalized homology theories on compact metric spaces
• A universal proper G-space
• Spaces over a category and assembly maps in isomorphism conjectures in \(K\)- and \(L\)-theory
• The relation between the Baum-Connes conjecture and the trace conjecture
• Perturbation theory for linear operators.
• The index of elliptic operators. III
• The signature operator at 2
• A special Stoke's theorem for complete Riemannian manifolds
• Chern characters for proper equivariant homology theories and applications to K- and L-theory
• The $K$-homology class of the Euler characteristic operator is trivial

This page was built for publication: Equivariant Euler characteristics and \(K\)-homology Euler classes for proper cocompact \(G\)-manifolds