Smooth K-Theory

Details Smooth K-Theory Smooth K-Theory

2007-06-30

arxiv.org/abs/0707.0046v4

Ast\'erisque 328 (2009), 45-135

Mathematics

K-Theory and Homology

v4 93 pages, version to appear in Asterisque (Bismut 60 proceedings)

Scientific paper

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.

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