Almost flat K-theory of classifying spaces

2015/03/20 by José R. Carrión, Carrión, José R., Marius Dadarlat +1 · 2 citations
Mathematics · #46L05 (primary) #46L80 #46L85 (secondary) #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05 #msc:46L80 #msc:46L85

paper · pdf · doi:10.48550/arxiv.1503.06170

24 pages, 4 figures

arxiv created 2015/03/20 · arxiv updated 2015/03/23

Abstract

We give a rigorous account and prove continuity properties for the correspondence between almost flat bundles on a triangularizable compact connected space and the quasi-representations of its fundamental group. For a discrete countable group Γ with finite classifying space BΓ, we study a correspondence between between almost flat K-theory classes on BΓ and group homomorphism K₀(C^*(Γ))→ ℤ that are implemented by pairs of discrete asymptotic homomorphisms from C^*(Γ) to matrix algebras.

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• Vanishing of Topological Invariants For Unnormalized Schatten p multiplicative Maps
• On Chern classes of almost representations

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