An infinite-dimensional index theorem and the Higson-Kasparov-Trout algebra
K-Theory and Homology
2022-06-22 v1 Differential Geometry
Functional Analysis
Operator Algebras
Abstract
We have been studying the index theory for some special infinite-dimensional manifolds with a "proper cocompact" actions of the loop group LT of the circle T, from the viewpoint of the noncommutative geometry. In this paper, we will introduce the LT-equivariant KK-theory and we will construct three KK-elements: the index element, the Clifford symbol element and the Dirac element. These elements satisfy a certain relation, which should be called the (KK-theoretical) index theorem, or the KK-theoretical Poincar\'e duality for infinite-dimensional manifolds. We will also discuss the assembly maps.
Keywords
Cite
@article{arxiv.1811.06811,
title = {An infinite-dimensional index theorem and the Higson-Kasparov-Trout algebra},
author = {Doman Takata},
journal= {arXiv preprint arXiv:1811.06811},
year = {2022}
}