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arXiv · 2204.00798

The Clifford Algebra Bundle on Loop Space

Matthias Ludewig
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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.

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Matthias Ludewig. 2022-04-02. The Clifford Algebra Bundle on Loop Space. https://doi.org/10.3842/sigma.2024.020

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