An equivariant index for proper actions II: properties and applications
Abstract
In the first part of this series, we defined an equivariant index without assuming the group acting or the orbit space of the action to be compact. This allowed us to generalise an index of deformed Dirac operators, defined for compact groups by Braverman. In this paper, we investigate properties and applications of this index. We prove that it has an induction property that can be used to deduce various other properties of the index. In the case of compact orbit spaces, we show how it is related to the analytic assembly map from the BaumConnes conjecture, and an index used by Mathai and Zhang. We use the index to define a notion of Khomological Dirac induction, and show that, under conditions, it satisfies the quantisation commutes with reduction principle.
 Publication:

arXiv eprints
 Pub Date:
 February 2016
 arXiv:
 arXiv:1602.02836
 Bibcode:
 2016arXiv160202836H
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Differential Geometry;
 Mathematics  Operator Algebras;
 Mathematics  Representation Theory
 EPrint:
 39 pages. The first version of preprint 1512.07575 was split up into two parts, this is the second part