The geometry of loop spaces II: Characteristic classes

Yoshiaki Maeda, Steven Rosenberg, Fabián Torres-Ardila

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    We develop a theory of Chern-Simons classes CS2k-1W∈H2k-1(LM2k-1;R) on the loop space LM of a Riemannian manifold M. These classes are associated to a pair of connections on LM whose connection and curvature forms take values in pseudodifferential operators by [19]. We use the Wodzicki residue of these operators to define and compute the Chern-Simons classes. As an application, we prove that |π1(Diff(M))|=∞ for the total space M of circle bundles associated to high multiples of a Kähler class over integral Kähler surfaces.

    Original languageEnglish
    Pages (from-to)485-518
    Number of pages34
    JournalAdvances in Mathematics
    Volume287
    DOIs
    Publication statusPublished - 2016 Jan 10

    Keywords

    • Characteristic classes
    • Diffeomorphism groups
    • Loop spaces
    • Pseudodifferential operators
    • Wodzicki residue

    ASJC Scopus subject areas

    • Mathematics(all)

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