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A Thom Isomorphism for Infinite Rank Euclidean Bundles | | Jody Trout
; | | Date: |
2 Jun 2003 | | Journal: | Homology, Homotopy, and Applications, 5 no. 1 (2003) 121-159 | | Subject: | K-Theory and Homology; Operator Algebras; Algebraic Topology; Functional Analysis MSC-class: Primary: 46L80, 19L47. Secondary: 58B05, 55R45 | math.KT math.AT math.FA math.OA | | Affiliation: | Dartmouth College | | Abstract: | An 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. | | Source: | arXiv, math.KT/0306048 | | Services: | Forum | Review | PDF | Favorites | |
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