The Geometry of Loop Spaces II: Characteristic Classes

2014/07/09 by Yoshiaki Maeda, Maeda, Yoshiaki, Steven Rosenberg +3 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1407.2491

openalex publication_date 2014/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the Wodzicki residue, we build Wodzicki-Chern-Simons (WCS) classes in H^2k-1(LM) associated to the residue Chern character on the loop space LM of a Riemannian manifold M^2k-1. These WCS classes are associated to the L² connection and the Sobolev s=1 connections on LM. The WCS classes detect several families of 5-manifolds whose isometry group has infinite fundamental group. These manifolds are the total spaces of the circle bundles associated to a multiple pω, |p|≫ 0, of the Kähler form ω over an integral Kähler surface.

Cited by

• The Geometry of Loop Spaces V: Fundamental Groups of Geometric Transformation Groups

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