کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661261 | 1344417 | 2006 | 23 صفحه PDF | دانلود رایگان |
Let M be a smooth Fredholm manifold modeled on a separable infinite-dimensional Euclidean space EE with Riemannian metric g . Given an augmented Fredholm filtration FF of M by finite-dimensional submanifolds {Mn}n=k∞, we associate to the triple (M,g,F)(M,g,F) a non-commutative direct limit C∗C∗-algebraA(M,g,F)=lim→A(Mn) that can play the role of the algebra of functions vanishing at infinity on the non-locally compact space M . The C∗C∗-algebra A(E)A(E), as constructed by Higson–Kasparov–Trout for their Bott periodicity theorem, is isomorphic to our construction when M=EM=E. If M has an oriented SpinqSpinq-structure (1⩽q⩽∞)(1⩽q⩽∞), then the K -theory of this C∗C∗-algebra is the same (with dimension shift) as the topological K-theory of M defined by Mukherjea. Furthermore, there is a Poincaré duality isomorphism of this K-theory of M with the compactly supported K-homology of M, just as in the finite-dimensional spin setting.
Journal: Topology and its Applications - Volume 153, Issue 14, 1 August 2006, Pages 2528–2550