Signature Operators and Surgery Groups over C*-algebras |
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Authors: | John G. Miller |
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Affiliation: | (1) Indiana University–Purdue University at Indianapolis, IN, 46202, U.S.A. e-mail |
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Abstract: | Let A be a unital complex C* algebra, L*(A) the projective symmetric surgery groups, and K*(A) topological K theory. We define groups B*(A) of bordism classes of Fredholm complexes over A with Poincaré duality. These generalize the de Rham complex. It is shown that there are isomorphisms B*(A)K* (A) and B*(A) L*(A) given by abstract versions of the signature operator and symmetric signature. The remaining side of a triangle is formed by an isomorphism due to Mienko. |
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Keywords: | Signature operator Wall groups algebraic surgery Fredholm complexes |
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