Relations between asymptotic and Fredholm representations

V. M. Manuilov; A. S. Mishchenko

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arXiv · funct-an/9707005

Relations between asymptotic and Fredholm representations

V. M. Manuilov·A. S. Mishchenko

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Abstract

We prove that for matrix algebras $M_n$ there exists a monomorphism $(\prod_n M_n/\oplus_n M_n)\otimes C(S^1) \to {\cal Q} $ into the Calkin algebra which induces an isomorphism of the $K_1$-groups. As a consequence we show that every vector bundle over a classifying space $Bπ$ which can be obtained from an asymptotic representation of a discrete group $π$ can be obtained also from a representation of the group $π\times Z$ into the Calkin algebra. We give also a generalization of the notion of Fredholm representation and show that asymptotic representations can be viewed as asymptotic Fredholm representations.

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BibTeX RIS

V. M. Manuilov, A. S. Mishchenko. 1997-07-16. Relations between asymptotic and Fredholm representations. https://arxiv.org/abs/funct-an/9707005

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