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• W1657243460 abstract "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 $mathbf{K}_*$-equivalence, where $mathbf{K}_*$ 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." @default.
• W1657243460 created "2016-06-24" @default.
• W1657243460 creator A5015915417 @default.
• W1657243460 date "2009-06-30" @default.
• W1657243460 modified "2023-09-27" @default.
• W1657243460 title "Noncommutative correspondence categories, simplicial sets and pro $C^*$-algebras" @default.
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• W1657243460 hasPublicationYear "2009" @default.
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