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arXiv · 1201.4593

Loop Differential K-theory

Thomas Tradler·Scott O. Wilson·Mahmoud Zeinalian
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Abstract

In this paper we introduce an equivariant extension of the Chern-Simons form, associated to a path of connections on a bundle over a manifold M, to the free loop space LM, and show it determines an equivalence relation on the set of connections on a bundle. We use this to define a ring, loop differential K-theory of M, in much the same way that differential K-theory can be defined using the Chern-Simons form [SS]. We show loop differential K-theory yields a refinement of differential K-theory, and in particular incorporates holonomy information into its classes. Additionally, loop differential K-theory is shown to be strictly coarser than the Grothendieck group of bundles with connection up to gauge equivalence. Finally, we calculate loop differential K-theory of the circle.

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BibTeXRIS

Thomas Tradler, Scott O. Wilson, Mahmoud Zeinalian. 2015-01-13. Loop Differential K-theory. https://arxiv.org/abs/1201.4593

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