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August 2019 K-theory and K-homology of finite wreath products with free groups
Sanaz Pooya
Illinois J. Math. 63(2): 317-334 (August 2019). DOI: 10.1215/00192082-7768735

Abstract

This article investigates an explicit description of the Baum–Connes assembly map of the wreath product Γ=FFn=FnFFn, where F is a finite and Fn is the free group on n generators. In order to do so, we take Davis–Lück’s approach to the topological side which allows computations by means of spectral sequences. Besides describing explicitly the K-groups and their generators, we present a concrete 2-dimensional model for the classifying space E̲Γ. As a result of our computations, we obtain that K0(Cr(Γ)) is the free abelian group of countable rank with a basis consisting of projections in Cr(FnF), and K1(Cr(Γ)) is the free abelian group of rank n with a basis represented by the unitaries coming from the free group.

Citation

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Sanaz Pooya. "K-theory and K-homology of finite wreath products with free groups." Illinois J. Math. 63 (2) 317 - 334, August 2019. https://doi.org/10.1215/00192082-7768735

Information

Received: 8 November 2018; Revised: 12 April 2019; Published: August 2019
First available in Project Euclid: 1 August 2019

zbMATH: 07088309
MathSciNet: MR3987499
Digital Object Identifier: 10.1215/00192082-7768735

Subjects:
Primary: 46L80
Secondary: 55R40

Rights: Copyright © 2019 University of Illinois at Urbana-Champaign

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Vol.63 • No. 2 • August 2019
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