The spinor bundle on loop space
Differential Geometry
2024-06-04 v5 Algebraic Topology
Operator Algebras
Abstract
We give a construction of the spinor bundle of the loop space of a string manifold together with its fusion product, inspired by ideas from Stolz and Teichner. The spinor bundle is a super bimodule bundle for a bundle of Clifford von Neumann algebras over the free path space, and the fusion product is defined using Connes fusion of such bimodules. As the main result, we prove that a spinor bundle with fusion product on a manifold X exists if and only X admits a string structure.
Cite
@article{arxiv.2305.12521,
title = {The spinor bundle on loop space},
author = {Matthias Ludewig},
journal= {arXiv preprint arXiv:2305.12521},
year = {2024}
}
Comments
Minor changes according to reviewer suggestions; restructured Sections 3.4 & 3.5