Equivariant-bivariant Chern character for profinite groups

P. Baum, P. Schneider

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

For the action of a locally compact and totally disconnected group G on a pair of locally compact spaces X and Y we construct, by sheaf theoretic means, a new equivariant and bivariant cohomology theory. If we take for the first space Y an universal proper G- action then we obtain for the second space its delocalized equivariant homology. This is in exact formal analogy to the definition of equivariant K-homology by Baum, Connes, Higson starting from the bivariant equivariant Kasparov K K -theory. Under certain basic finiteness conditions on the first space Y we conjecture the existence of a Chern character from the equivariant Kasparov K K -theory of Y and X into our cohomology theory made two-periodic which becomes an isomorphism upon tensoring the K K-theory with the complex numbers. This conjecture is proved for profinite groups G. An essential role in our construction is played by a bivariant version of Segal localization which we establish for K K -theory.

Original languageEnglish (US)
Pages (from-to)313-353
Number of pages41
JournalK-Theory
Volume25
Issue number4
DOIs
StatePublished - Dec 1 2002

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Chern Character
Profinite Groups
Equivariant
K-theory
Cohomology
K-homology
Locally Compact Space
Finiteness Conditions
Locally Compact
Complex number
Sheaves
Analogy
Homology
Isomorphism

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Baum, P. ; Schneider, P. / Equivariant-bivariant Chern character for profinite groups. In: K-Theory. 2002 ; Vol. 25, No. 4. pp. 313-353.
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Equivariant-bivariant Chern character for profinite groups. / Baum, P.; Schneider, P.

In: K-Theory, Vol. 25, No. 4, 01.12.2002, p. 313-353.

Research output: Contribution to journalArticle

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