A Short Proof of the Localization Formula for the Loop Space Chern Character of Spin Manifolds

TL;DR

This paper provides a concise proof of the localization formula for the loop space Chern character on spin manifolds, utilizing the rescaled spinor bundle on the tangent groupoid.

Contribution

It introduces a simplified proof of the localization formula for the loop space Chern character using geometric structures on the tangent groupoid.

Findings

Short proof of the localization formula established

Rescaled spinor bundle technique applied

Simplifies previous approaches to the localization formula

Abstract

In this note, we give a short proof of the localization formula for the loop space Chern character of a compact Riemannian spin manifold M, using the rescaled spinor bundle on the tangent groupoid associated to M.