S¹-equivariant Chern-Weil constructions on loop space

2015/07/30 by McCauley, Thomas
#55R91 (Secondary) #57R91 (Primary) #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1507.08626

Abstract

We study the existence of S¹-equivariant characteristic classes on certain natural infinite rank bundles over the loop space LM of a manifold M. We discuss the different S¹-equivariant cohomology theories in the literature and clarify their relationships. We attempt to use S¹-equivariant Chern-Weil techniques to construct S¹-equivariant characteristic classes. The main result is the construction of a sequence of S¹-equivariant characteristic classes on the total space of the bundles, but these classes do not descend to the base LM. Nevertheless, we conclude by identifying a class of bundles for which the S¹-equivariant first Chern class does descend to LM.

Cited by

• Equivariant, string and leading order characteristic classes associated to fibrations
• Traces and Characteristic Classes in Infinite Dimensions

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