Equivariant geometric K-homology for compact lie group actions

Paul Baum; Hervé Oyono-Oyono; Thomas Schick; Michael Walter

doi:10.1007/s12188-010-0034-z

Equivariant geometric K-homology for compact lie group actions

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

Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

Let G be a compact Lie-group, X a compact G-CW-complex.We define equivariant geometric K-homology groups K_*^G(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology.We define explicit natural transformations to and from equivariant K-homology defined via KK-theory (the "official" equivariant K-homology groups) and show that these are isomorphisms.

Original language	English (US)
Pages (from-to)	149-173
Number of pages	25
Journal	Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume	80
Issue number	2
DOIs	https://doi.org/10.1007/s12188-010-0034-z
State	Published - 2010

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s12188-010-0034-z

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title = "Equivariant geometric K-homology for compact lie group actions",

abstract = "Let G be a compact Lie-group, X a compact G-CW-complex.We define equivariant geometric K-homology groups K*G(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology.We define explicit natural transformations to and from equivariant K-homology defined via KK-theory (the {"}official{"} equivariant K-homology groups) and show that these are isomorphisms.",

author = "Paul Baum and Herv{\'e} Oyono-Oyono and Thomas Schick and Michael Walter",

note = "Funding Information: Research of P. Baum partially supported by the Polish Government grant N201 1770 33 and by an NSF research grant. Research of T. Schick partially funded by the Courant Research Center “Higher order structures in Mathematics” within the German initiave of excellence.",

year = "2010",

doi = "10.1007/s12188-010-0034-z",

language = "English (US)",

volume = "80",

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journal = "Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg",

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T1 - Equivariant geometric K-homology for compact lie group actions

AU - Baum, Paul

AU - Oyono-Oyono, Hervé

AU - Schick, Thomas

AU - Walter, Michael

N1 - Funding Information: Research of P. Baum partially supported by the Polish Government grant N201 1770 33 and by an NSF research grant. Research of T. Schick partially funded by the Courant Research Center “Higher order structures in Mathematics” within the German initiave of excellence.

PY - 2010

Y1 - 2010

N2 - Let G be a compact Lie-group, X a compact G-CW-complex.We define equivariant geometric K-homology groups K*G(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology.We define explicit natural transformations to and from equivariant K-homology defined via KK-theory (the "official" equivariant K-homology groups) and show that these are isomorphisms.

AB - Let G be a compact Lie-group, X a compact G-CW-complex.We define equivariant geometric K-homology groups K*G(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology.We define explicit natural transformations to and from equivariant K-homology defined via KK-theory (the "official" equivariant K-homology groups) and show that these are isomorphisms.

UR - https://www.scopus.com/pages/publications/84893704796

UR - https://www.scopus.com/pages/publications/84893704796#tab=citedBy

U2 - 10.1007/s12188-010-0034-z

DO - 10.1007/s12188-010-0034-z

M3 - Article

AN - SCOPUS:84893704796

SN - 0025-5858

VL - 80

SP - 149

EP - 173

JO - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

JF - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

IS - 2

ER -

Equivariant geometric K-homology for compact lie group actions

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