The geometry of loop spaces I: Hs-Riemannian metrics

Yoshiaki Maeda, Steven Rosenberg, Fabián Torres-Ardila

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    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. We compute the connection forms of these metrics and the higher symbols of their curvature forms, which take values in pseudodifferential operators (ΨDOs). These calculations are used in the followup paper [10] to construct Chern-Simons classes on TLM which detect nontrivial elements in the diffeomorphism group of certain Sasakian 5-manifolds associated to Kähler surfaces.

    Original languageEnglish
    Article number1540002
    JournalInternational Journal of Mathematics
    Volume26
    Issue number4
    DOIs
    Publication statusPublished - 2015 Mar 25

    Keywords

    • Levi-Civita connections
    • Loop spaces
    • pseudodifferential operators

    ASJC Scopus subject areas

    • Mathematics(all)

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