The Clifford Algebra Bundle on Loop Space
Differential Geometry
2024-03-13 v4 Algebraic Topology
Operator Algebras
Abstract
We construct a Clifford algebra bundle formed from the tangent bundle of the smooth loop space of a Riemannian manifold, which is a bundle of super von Neumann algebras on the loop space. We show that this bundle is in general non-trivial, more precisely that its triviality is obstructed by the transgressions of the second Stiefel-Whitney class and the first (fractional) Pontrjagin class of the manifold.
Cite
@article{arxiv.2204.00798,
title = {The Clifford Algebra Bundle on Loop Space},
author = {Matthias Ludewig},
journal= {arXiv preprint arXiv:2204.00798},
year = {2024}
}