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The geometry of loop spaces II: Characteristic classes

Maeda, Yoshiaki; Rosenberg, Steven; Torres-Ardila, Fabián

Advances in mathematics -- Elsevier Science -- Volume: 287 C; (pages 485-518) -- 2016

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  • Title:
    The geometry of loop spaces II: Characteristic classes
  • Author: Maeda, Yoshiaki;
    Rosenberg, Steven;
    Torres-Ardila, Fabián
  • Found In: Advances in mathematics. Volume 287:Number C(2016); 20160110; 485-518
  • Journal Title: Advances in mathematics
  • Subjects: Mathematics; LCSH: Mathematics; Dewey: 510
  • Rights: Licensed
  • Publication Details: Elsevier Science
  • Abstract: AbstractWe develop a theory of Chern–Simons classesCS2k1WH2k1(LM2k1;R)on the loop spaceLMof a Riemannian manifoldM. These classes are associated to a pair of connections onLMwhose 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 spaceMof circle bundles associated to high multiples of a Kähler class over integral Kähler surfaces.HighlightsCharacteristic classes on loop spaces are introduced to study diffeomorphism groups of certain 5-manifolds.The characteristic classes use the Wodzicki residue of pseudodifferential operators.The primary characteristic classes vanish, but the secondary Chern–Simons classes can be nontrivial.
  • Identifier: Journal ISSN: 0001-8708
  • Publication Date: 2016
  • Physical Description: Electronic
  • Shelfmark(s): 0709.370000
  • UIN: ETOCvdc_100042766881.0x000001

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