Smooth K-Theory
K-Theory and Homology
2010-09-13 v4 Differential Geometry
Abstract
We construct an analytic multiplicative model of smooth K-theory. We further introduce the notion of a smooth K-orientation of a proper submersion and define the associated push-forward which satisfies functoriality, compatibility with pull-back diagrams, and projection and bordism formulas. We construct a multiplicative lift of the Chern character from smooth K-theory to smooth rational cohomology and verify that the cohomological version of the Atiyah-Singer index theorem for families lifts to smooth cohomology.
Cite
@article{arxiv.0707.0046,
title = {Smooth K-Theory},
author = {Ulrich Bunke and Thomas Schick},
journal= {arXiv preprint arXiv:0707.0046},
year = {2010}
}