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general linear group of a banach algebra

Journal of K-Theory (1)

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Spaces of sections of Banach algebra bundles
Emmanuel Dror Farjoun, Claude L. Schochet
Journal:

Journal of K-Theory / Volume 10 / Issue 2 / October 2012

Published online by Cambridge University Press:

04 April 2012, pp. 279-298

Print publication:

October 2012
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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.