Algebra cochains, the bivariant JLO cocycle and the Mathai-Quillen form
K-Theory and Homology
2022-11-09 v1
Abstract
This is a first investigation by the author of the similarity between Quillen's superconnection formalism, his constructions of (periodic) cyclic cocycles via algebra cochains on a bar construction, and Kasparov bimodules for KK-theory. In this article, we do so by deriving a slight extension of the Mathai-Quillen Thom form via a bivariant JLO cocycle. The main idea (which is in fact not really new) is that KK-cycles should be thought of as superconnection forms; these methods will be applied to other contexts elsewhere.
Cite
@article{arxiv.2211.03996,
title = {Algebra cochains, the bivariant JLO cocycle and the Mathai-Quillen form},
author = {Rudy Rodsphon},
journal= {arXiv preprint arXiv:2211.03996},
year = {2022}
}