Traces and characteristic classes in infinite dimensions

Yoshiaki Maeda, Steven Rosenberg

    研究成果: Chapter

    2 被引用数 (Scopus)

    抄録

    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.

    本文言語English
    ホスト出版物のタイトルProgress in Mathematics
    出版社Springer Basel
    ページ413-435
    ページ数23
    DOI
    出版ステータスPublished - 2015 1月 1

    出版物シリーズ

    名前Progress in Mathematics
    308
    ISSN(印刷版)0743-1643
    ISSN(電子版)2296-505X

    ASJC Scopus subject areas

    • 分析
    • 代数と数論
    • 幾何学とトポロジー

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