Illinois Journal of Mathematics

K-theory and K-homology of finite wreath products with free groups

Sanaz Pooya

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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.

Article information

Source
Illinois J. Math., Volume 63, Number 2 (2019), 317-334.

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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1564646437

Digital Object Identifier
doi:10.1215/00192082-7768735

Mathematical Reviews number (MathSciNet)
MR3987499

Zentralblatt MATH identifier
07088309

Subjects
Primary: 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
Secondary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]

Citation

Pooya, Sanaz. K-theory and K-homology of finite wreath products with free groups. Illinois J. Math. 63 (2019), no. 2, 317--334. doi:10.1215/00192082-7768735. https://projecteuclid.org/euclid.ijm/1564646437


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References

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