Homotopy invariance through small stabilizations

Abstract

We associate an algebra Γ∞(A) to each bornological algebra A . Each symmetric ideal SS of the algebra ℓ∞ of complex bounded sequences gives rise to an ideal IS(A) of Γ∞(A) . We show that all ideals arise in this way when AA is the algebra of complex numbers. We prove that for suitable S , Weibel’s K -theory of IS(A) is homotopy invariant, and show that the failure of the map from Quillen’s to Weibel’s K -theory of IS(A) to be an isomorphism is measured by cyclic homology.