Shapiro's lemma for topological K-theory of groups | Zendy

J. Chabert | Zendy; Siegfried Echterhoff | Zendy; Hervé OyonoOyono | Zendy

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Shapiro's lemma for topological K-theory of groups

Author(s) -

J. Chabert,

Siegfried Echterhoff,

Hervé OyonoOyono

Publication year - 2003

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140300009

Subject(s) - mathematics , lemma (botany) , topological group , pure mathematics , topology (electrical circuits) , combinatorics , ecology , poaceae , biology

Let X oG be the crossed product groupoid of a locally compact group G acting on a locally compact space X. For any X oG-algebra A we show that a natural forgetful map from the topological K-theory K top (X o G;A) of the groupoid X o G with coe-cients in A to the topological K-theory K top (G;A )o f Gwith coe-cients in A is an isomorphism. We then discuss several interesting consequences of this result for the Baum{Connes conjecture. Mathematics Subject Classiflcation (2000). 19K35, 19KXX, 46L80 (Primary), 22D15, 22A22 (Secondary).

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