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arXiv · 0707.0046

Smooth K-Theory

Ulrich Bunke·Thomas Schick
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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.

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Ulrich Bunke, Thomas Schick. 2009-05-16. Smooth K-Theory. https://arxiv.org/abs/0707.0046

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