Traces and characteristic classes in infinite dimensions

Yoshiaki Maeda, Steven Rosenberg

    Research output: Chapter in Book/Report/Conference proceedingChapter

    2 Citations (Scopus)

    Abstract

    We survey geometric constructions of characteristic classes associated to certain infinite rank bundles on the loop space LM of a manifold M. There are two types of classes, which arise from applying either the leading order trace or the Wodzicki residue to the curvature of natural connections on TLM, as the curvature forms take values in pseudodifferential operators. The leading order classes lead to a restatement of the S1-index theorem on LM, provide generators for the cohomology of loop groups, and for Maps(S2,M) are related to Gromov-Witten invariants. The Wodzicki classes have applications to the topology of diffeomorphism groups of certain circle bundles over Kaehler surfaces.

    Original languageEnglish
    Title of host publicationProgress in Mathematics
    PublisherSpringer Basel
    Pages413-435
    Number of pages23
    DOIs
    Publication statusPublished - 2015 Jan 1

    Publication series

    NameProgress in Mathematics
    Volume308
    ISSN (Print)0743-1643
    ISSN (Electronic)2296-505X

    Keywords

    • Characteristic classes
    • Loop space
    • Wodzizki trace

    ASJC Scopus subject areas

    • Analysis
    • Algebra and Number Theory
    • Geometry and Topology

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