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On C*-algebras and K-theory for infinite-dimensional Fredholm Manifolds | | Dorin Dumitrascu
; Jody Trout
; | | Date: |
22 Nov 2004 | | Subject: | Operator Algebras; Algebraic Topology; Functional Analysis; K-Theory and Homology MSC-class: 19, 46, 47, 55, 57, 58 | math.OA math.AT math.FA math.KT | | Affiliation: | University of Arizona) and Jody Trout (Dartmouth College | | Abstract: | Let M be a smooth Fredholm manifold modeled on a separable infinite-dimensional Euclidean space E with Riemannian metric g. Given an (augmented) Fredholm filtration F of M by finite-dimensional submanifolds (M_n), we associate to the triple (M, g, F) a non-commutative direct limit C*-algebra A(M, g, F) = lim A(M_n) that can play the role of the algebra of functions vanishing at infinity on the non-locally compact space M. The C*-algebra A(E), as constructed by Higson-Kasparov-Trout for their Bott periodicity theorem for infinite dimensional Euclidean spaces, is isomorphic to our construction when M = E. If M has an oriented Spin_q-structure (1 <= q <=infty), then the K-theory of this C*-algebra is the same (with dimension shift) as the topological K-theory of M defined by Mukherjea. Furthermore, there is a Poincare’ duality isomorphism of this K-theory of M with the compactly supported K-homology of M, just as in the finite-dimensional spin setting. | | Source: | arXiv, math.OA/0411495 | | Services: | Forum | Review | PDF | Favorites | |
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