A regulator for smooth manifolds and an index theorem
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.
Keywords
Cite
@article{arxiv.1407.1379,
title = {A regulator for smooth manifolds and an index theorem},
author = {Ulrich Bunke},
journal= {arXiv preprint arXiv:1407.1379},
year = {2014}
}
Comments
49 pages (Proofs of the main theorems considerably simplified by using a better adapted version of differential connective K-theory)