The Analytical Assembly Map and Index Theory
K-Theory and Homology
2014-03-07 v2 Algebraic Topology
Operator Algebras
Abstract
In this paper we study the index theoretic interpretation of the analytical assembly map that appears in the Baum-Connes conjecture. In its general form it may be constructed using Kasparov's equivariant KK-theory. In the special case of a torsionfree group the domain simplifies to the usual K-homology of the classifying space BG of G and it is frequently used that in this case the analytical assembly map is given by assigning to an operator an equivariant index. We give a precise formulation of this statement and prove it.
Cite
@article{arxiv.1306.5657,
title = {The Analytical Assembly Map and Index Theory},
author = {Markus Land},
journal= {arXiv preprint arXiv:1306.5657},
year = {2014}
}
Comments
13 pages, revised and shorter version