Secondary Characteristic Classes on Loop Spaces

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.

Revised version of the paper "Riemannian Geometry on Loop Spaces." This version handles noninteger Sobolev parameters

Cited by in corpus (4)

• Equivariant, string and leading order characteristic classes associated to fibrations
• The order of curvature operators on loop groups
• Chern-Weil calculus extended to a class of infinite dimensional manifolds
• K-Theories for Certain Infinite Rank Bundles