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arXiv · 1407.1379

A regulator for smooth manifolds and an index theorem

Ulrich Bunke
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Abstract

For a smooth manifold X of dimension <d we construct a homomorphism from the algebraic K-theory group in degree d of the algebra of smooth functions on X to the degree -d-1 topological K-theory of X with coefficients in C/Z. This map generalizes the map used by Suslin in order to calculate the torsion subgroup of algebraic K-theory of C (the case X=*). We state and partially prove a conjecture which compares the composition of the map above with the evaluation against the K-homology class of a Dirac operator on X on the one hand, and the Connes-Karoubi multiplicative character of the associated d-summable Fredholm module on the other.

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Ulrich Bunke. 2014-12-08. A regulator for smooth manifolds and an index theorem. https://arxiv.org/abs/1407.1379

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