Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 63, Number 2 (2019), 317-334.
K-theory and K-homology of finite wreath products with free groups
This article investigates an explicit description of the Baum–Connes assembly map of the wreath product , where is a finite and is the free group on 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 . As a result of our computations, we obtain that is the free abelian group of countable rank with a basis consisting of projections in , and is the free abelian group of rank with a basis represented by the unitaries coming from the free group.
Illinois J. Math., Volume 63, Number 2 (2019), 317-334.
Received: 8 November 2018
Revised: 12 April 2019
First available in Project Euclid: 1 August 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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