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arXiv · 0705.1008

Secondary Characteristic Classes on Loop Spaces

Yoshiaki Maeda·Steven Rosenberg·Fabián Torres-Ardila
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Abstract

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. The connection and curvature forms of these metrics take values in pseudodifferential operators. We develop a theory of Wodzicki-Chern-Simons classes using the s=0, 1 connections and the Wodzicki residue. These classes distinguish the smooth homotopy type of some circle actions on M = S^2 x S^3, and imply that the fundamental group of Diff(M) is infinite.

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Yoshiaki Maeda, Steven Rosenberg, Fabián Torres-Ardila. 2012-10-25. Secondary Characteristic Classes on Loop Spaces. https://arxiv.org/abs/0705.1008

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