An Index Theorem for Loop Spaces
K-Theory and Homology
2022-08-26 v1 Mathematical Physics
Differential Geometry
math.MP
Operator Algebras
Abstract
We formulate and prove an index theorem for loop spaces of compact manifolds in the framework of -theory. It is a strong candidate for the noncommutative geometrical definition (or the analytic counterpart) of the Witten genus. In order to find out an "appropriate form" of the index theorem to formulate a loop space version, we formulate and prove an equivariant index theorem for non-compact manifolds equipped with -actions with compact fixed-point sets. In order to formulate it, we use a ring of formal power series.
Cite
@article{arxiv.2208.12129,
title = {An Index Theorem for Loop Spaces},
author = {Doman Takata},
journal= {arXiv preprint arXiv:2208.12129},
year = {2022}
}
Comments
41 pages