Secondary Characteristic Classes on Loop Spaces
Differential Geometry
2012-10-26 v5 Analysis of PDEs
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.
Cite
@article{arxiv.0705.1008,
title = {Secondary Characteristic Classes on Loop Spaces},
author = {Yoshiaki Maeda and Steven Rosenberg and Fabián Torres-Ardila},
journal= {arXiv preprint arXiv:0705.1008},
year = {2012}
}