Ring and module structures on $K$-theory of leaf spaces and their application to longitudinal index theory
K-Theory and Homology
2017-05-17 v2
Abstract
Pursuing conjectures of John Roe, we use the stable Higson corona of foliated cones to construct a new -theory model for the leaf space of a foliation. This new -theory model is -- in contrast to Alain Connes' -theory model -- a ring. We show that Connes' -theory model is a module over this ring and develop an interpretation of the module multiplication in terms of indices of twisted longitudinally elliptic operators.
Keywords
Cite
@article{arxiv.1510.04470,
title = {Ring and module structures on $K$-theory of leaf spaces and their application to longitudinal index theory},
author = {Christopher Wulff},
journal= {arXiv preprint arXiv:1510.04470},
year = {2017}
}
Comments
Accepted for publication by the Journal of Topology