Infinite Dimensional Chern-Simons Theory

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dc.creatorRosenberg, Steven
dc.creatorTorres-Ardila, Fabian
dc.date2004-11-08
dc.date.accessioned2026-07-07T05:14:04Z
dc.date.available2026-07-07T05:14:04Z
dc.descriptionWe extend finite dimensional Chern-Simons theory to certain infinite dimensional principal bundles with connections, in particular to the frame bundle $FLM\to LM$ over the loop space of a Riemannian manifold $M$. Chern-Simons forms are defined roughly as in finite dimensions with the invariant polynomials replaced by appropriate Wodzicki residues. This produces odd dimensional $\R/\Z$-valued cohomology classes on $LM$ if $M$ is parallelizable. We compute an example of a metric on the loop space of $S^3\times S^1$ for which the three dimensional Chern-Simons class is nontrivial.
dc.identifierhttps://arxiv.org/abs/math/0411161
dc.identifierhttp://arxiv.org/abs/math/0411161
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73141
dc.subjectDifferential Geometry
dc.subject58B20
dc.titleInfinite Dimensional Chern-Simons Theory
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