The Clifford Algebra Bundle on Loop Space
Matthias Ludewig

TL;DR
This paper constructs a Clifford algebra bundle over the loop space of a Riemannian manifold, revealing its non-triviality is linked to topological invariants like Stiefel-Whitney and Pontrjagin classes.
Contribution
It introduces a new Clifford algebra bundle on loop space and identifies topological obstructions to its triviality.
Findings
The bundle is generally non-trivial.
Triviality is obstructed by transgressed Stiefel-Whitney and Pontrjagin classes.
Links topological invariants to algebraic bundle properties.
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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry · Advanced Operator Algebra Research
