\(K\)-theory of fine topological algebras, Chern character, and assembly
type: Item
instance of: scholarly article
title: \(K\)-theory of fine topological algebras, Chern character, and assembly
zbMATH Open document ID: 0776.19005
DOI: 10.1007/BF00961335
author: U. Tillmann
published in: \(K\)-Theory
publication date: 1993-04-01T00:00:00Z
review text: Let \(\Gamma\) be a countable discrete group with classifying space \(B\Gamma\). Let \(\mathbb{C}[\Gamma]\) be the group ring of \(\Gamma\) with the fine topology (that is, \(\mathbb{C}[\Gamma]\) is the colimit of its finite- dimensional subspaces). The author shows that the assembly map \(K_ * B\Gamma\to K_ *\mathbb{C}[\Gamma]\) in \(K\)-theory is a rational injection. The proof involves constructing a Chern character for fine topological algebras and showing that it is multiplicative. The paper includes a lot of background material.
Mathematics Subject Classification ID: 19D55
Mathematics Subject Classification ID: 57R19
zbMATH DE Number: 149766
zbMATH Keywords: Novikov conjecture
zbMATH Keywords: fine topology
zbMATH Keywords: assembly map
zbMATH Keywords: Chern character
zbMATH Keywords: fine topological algebras
reviewed by: Richard John Steiner
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 149766