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A regulator for smooth manifolds and an index theorem

Bunke, Ulrich


For a smooth manifold X and an integer d > dim(X) we construct and investigate a natural map sigma(d) : K-d (C-infinity (X)) -> ku C/Z(-d-1)(X). Here K-d (C-infinity(X)) is the algebraic K-theory group of the algebra of complex valued smooth functions on X, and ku C/Z* is the generalized cohomology theory called connective complex K-theory with coefficients in C/Z. If the manifold X is closed of ...


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