A Thom Isomorphism for Infinite Rank Euclidean Bundles

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dc.creatorTrout, Jody
dc.date2003-06-02
dc.date.accessioned2026-07-07T04:58:31Z
dc.date.available2026-07-07T04:58:31Z
dc.descriptionAn equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a non-commutative C*-algebra associated to a bundle E -> M, equipped with a compatible connection, which plays the role of the algebra of functions on the infinite dimensional total space E. If the base M is a point, we obtain the Bott periodicity isomorphism theorem of Higson-Kasparov-Trout for infinite dimensional Euclidean spaces. The construction applied to an even (finite rank) spin-c-bundle over an even-dimensional proper spin-c-manifold reduces to the classical Thom isomorphism in topological K-theory. The techniques involve non-commutative geometric functional analysis.
dc.descriptionAccepted for publication in Homology, Homotopy and Applications
dc.identifierhttps://arxiv.org/abs/math/0306048
dc.identifierhttp://arxiv.org/abs/math/0306048
dc.identifierHomology, Homotopy, and Applications, 5 no. 1 (2003) 121-159
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67669
dc.subjectK-Theory and Homology
dc.subjectAlgebraic Topology
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subjectPrimary: 46L80, 19L47. Secondary: 58B05, 55R45
dc.titleA Thom Isomorphism for Infinite Rank Euclidean Bundles
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