The Clifford Algebra Bundle on Loop Space
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Published:2024-03-12
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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Short-container-title:SIGMA
Author:
,Ludewig Matthias, ,
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.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)