Equivariant geometric K-homology for compact Lie group actions

DOI10.1007/s12188-010-0034-zzbMath1242.19006arXiv0902.0641OpenAlexW3100280699WikidataQ115377305 ScholiaQ115377305MaRDI QIDQ609393

Paul F. Baum, Hervé Oyono-Oyono, Michael Walter, Thomas Schick

Publication date: 30 November 2010

Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.0641

zbMATH Keywords

equivariant K-homologyequivariant \((M,E,f)\)equivariant Baum-Douglas cyclesG-CW-complexgeometric K-homologyGysin homomorphism in equivariant K-theoryPoincaré duality in equivariant K-theory

Mathematics Subject Classification ID

Generalized (extraordinary) homology and cohomology theories in algebraic topology (55N20) Ext and (K)-homology (19K33) Kasparov theory ((KK)-theory) (19K35) Equivariant (K)-theory (19L47) Index theory (19K56)

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Cites Work

• Unnamed Item
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• Equivariant embeddings in euclidean space
• On the equivalence of geometric and analytic \(K\)-homology
• The longitudinal index theorem for foliations
• Equivariant KK-theory and the Novikov conjecture
• Groups acting on buildings, operator \(K\)-theory, and Novikov's conjecture
• The Novikov conjecture for hyperbolic foliations
• A bordism-type description of homology
• Bivariant K-theory via correspondences
• The equivariant homotopy type of \(G-ANR\)'s for compact group actions
• Clifford modules
• Equivariant K-theory
• A Geometric Description of Equivariant K-Homology for Proper Actions
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• TOPOLOGICAL INVARIANTS OF ELLIPTIC OPERATORS. I:K-HOMOLOGY
• BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS
• Spaces With a Compact Lie Group of Transformations

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