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.
Keywords:loop spaces, Clifford algebra, string geometry, von Neumann algebra bundles.
Fulltext:
PDF file (530 kB)