2009/06/30 by Snigdhayan Mahanta, Mahanta, Snigdhayan
Mathematics · #18E30 #19K35 #55P57 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.0906.5400
openalex publication_date 2009/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that a KK-equivalence between two unital C^*-algebras produces a correspondence between their DG categories of finitely generated projective modules which is a K_*-equivalence, where K_* is Waldhausen's K-theory. We discuss some connections with strong deformations of C^*-algebras and homological dualities. Motivated by a construction of Cuntz we associate a pro C^*-algebra to any simplicial set. We show that this construction is functorial with respect to proper maps of simplicial sets, that we define, and also respects proper homotopy equivalences. We propose to develop a noncommutative proper homotopy theory in the context of topological algebras.