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The Clifford Algebra Bundle on Loop Space (2204.00798v4)
Published 2 Apr 2022 in math.DG, math.AT, and math.OA
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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