2011/01/03 by Emmanuel Dror Farjoun, Farjoun, Emmanuel Dror, Claude L. Schochet +1
Mathematics · #46L80 #46L85 #46M20 #55Q52 #55R20 #55T25 #Algebraic Topology (math.AT) #FOS: Mathematics #Operator Algebras (math.OA) #math.AT #math.OA #msc:46L80 #msc:46L85 #msc:46M20 #msc:55Q52 #msc:55R20 #msc:55T25
paper · pdf · doi:10.48550/arxiv.1101.0444
15 pages. Results generalized to include both real and complex K-theory. To appear in J. K-Theory
arxiv created 2012/01/11 · arxiv updated 2012/01/12
Suppose that B is a G-Banach algebra over \mathbbF = 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 ×G B) is the associated algebra of sections. We produce a spectral sequence which converges to π_*(GLo Aζ) with [E2-p,q ≅ \checkHp(X ; πq(GLo B)).] 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_*(GLo B) → \K*+1(B) is an isomorphism for all *>0) then so is Aζ.