Spaces of Sections of Banach Algebra Bundles

Authors

Emmanuel Dror Farjoun, Hebrew University of Jerusalem
Claude Schochet, Wayne State UniversityFollow

Document Type

Article

Abstract

Suppose that B is a G-Banach algebra over 𝔽 = ℝ or ℂ, X is a finite dimensional compact metric space, ζ : P → X is a standard principal G-bundle, and A_ζ = Γ(X,P x_G B) is the associated algebra of sections. We produce a spectral sequence which converges to π_∗(GL_oA_ζ) with

E_{_}²_p,q ≅ Ȟ^p(X ; π_q(GL_oB)).

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

Disciplines

Algebra | Analysis | Physical Sciences and Mathematics

Comments

Copyright © 2012 Cambridge University Press

Recommended Citation

E. Dror Farjouin and C. Schochet, Spaces of sections of Banach algebra bundles, Journal of K-Theory 10.2 (2012), 279-298. doi:10.1017/is012002001jkt183