An identification of the Baum-Connes and Davis-L\"uck assembly maps
K-Theory and Homology
2022-02-01 v2 Operator Algebras
Abstract
The Baum-Connes conjecture predicts that a certain assembly map is an isomorphism. We identify the homotopy theoretical construction of the assembly map by Davis and L\"uck with the category theoretical construction by Meyer and Nest. This extends the result of Hambleton and Pedersen to arbitrary coefficients. Our approach uses abstract properties rather than explicit constructions and is formally similar to Meyer's and Nest's identification of their assembly map with the original construction of the assembly map by Baum, Connes and Higson.
Cite
@article{arxiv.2009.11964,
title = {An identification of the Baum-Connes and Davis-L\"uck assembly maps},
author = {Julian Kranz},
journal= {arXiv preprint arXiv:2009.11964},
year = {2022}
}
Comments
26 pages. Added references. The arguments of Section 6 were simplified. Final version