Secondary Characteristic Classes on Loop Spaces

2007/05/07 by Yoshiaki Maeda, Maeda, Yoshiaki, Steven Rosenberg +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.0705.1008

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

arxiv created 2012/10/25 · arxiv updated 2012/10/26

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 = S² x S³, and imply that the fundamental group of Diff(M) is infinite.

Cited by

• The Geometry of Loop Spaces I: H^s-Riemannian Metrics

Related

• The Geometry of Loop Spaces I: H^s-Riemannian Metrics
• The Geometry of Loop Spaces II: Characteristic Classes
• Traces and Characteristic Classes in Infinite Dimensions
• H-Space and Loop Space Structures for Intermediate Curvatures
• The Geometry of Loop Spaces III: Isometry Groups of Contact Manifolds