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The Geometry of Loop Spaces I: $H^s$-Riemannian Metrics

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arxiv 1405.4231 v1 pith:3X5AABQF submitted 2014-05-16 math.DG

Yoshiaki Maeda , Steven Rosenberg , Fabián Torres-Ardila This is my paper · ORCID
classification math.DG
keywords loopmetricsriemannianclassesformsgeometryspacespaces
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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. These calculations are used in a followup paper "The Geometry of Loop Spaces II: Characteristic Classes" to construct Chern-Simons classes on the tangent bundle TLM which detect nontrivial elements in the diffeomorphism group of certain Sasakian 5-manifolds associated to Kaehler surfaces.

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  1. Exotic gravity theory in loop space

    hep-th 2024-12 conditional novelty 5.0 of 10

    Hull's exotic C-field and its curvature G are reformulated as an ultra-local metric and curvature on loop space.

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