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Spaces of sections of Banach algebra bundles

Published online by Cambridge University Press:  04 April 2012

Emmanuel Dror Farjoun  and
Claude L. Schochet
Emmanuel Dror Farjoun
Affiliation:
Department of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904, Israel, farjoun@huji.ac.il
Claude L. Schochet
Affiliation:
Department of Mathematics, Wayne State University, Detroit MI 48202, claude@math.wayne.edu
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Abstract

Suppose that B is a G-Banach algebra over = ℝ or ℂ X is a finite dimensional compact metric space, ζ : P → X is a standard principal G-bundle, and Aζ = Γ(X,P ×GB) is the associated algebra of sections. We produce a spectral sequence which converges to π*(GLoAζ) with

A related spectral sequence converging to K*+1(Aζ) (the real or complex topological K-theory) allows us to conclude that if B is Bott-stable, (i.e., if π*(GLoB) → K*+1(B) is an isomorphism for all * > 0) then so is Aζ.

Keywords

general linear group of a Banach algebraspectral sequenceslocalizationBott-stableK-theory for Banach algebrasunstable K-theory

Information

Type
Research Article
Information
Journal of K-Theory , Volume 10 , Issue 2 , October 2012 , pp. 279 - 298
Copyright
Copyright © ISOPP 2012

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