\(K\)-theory of fine topological algebras, Chern character, and assembly
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.
scientific article; zbMATH DE number 149766
scientific article