2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67669An 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.Accepted for publication in Homology, Homotopy and ApplicationsK-Theory and HomologyAlgebraic TopologyFunctional AnalysisOperator AlgebrasPrimary: 46L80, 19L47. Secondary: 58B05, 55R45text