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Spaces Of Sections Of Banach Algebra Bundles, Emmanuel Dror Farjoun, Claude Schochet

Mathematics Faculty Research Publications

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 …