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Smooth K-Theory

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arxiv 0707.0046 v4 pith:PZFETGKI submitted 2007-06-30 math.KT math.DG

Ulrich Bunke (Regensburg) , Thomas Schick (Georg-August-Universitaet Goettingen) This is my paper · ORCID
classification math.KTmath.DG
keywords smoothk-theorycohomologyconstructmultiplicativeanalyticassociatedatiyah-singer
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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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Cited by 1 Pith paper

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  1. Differential Models for the Anderson Dual to Twisted $\mathrm{Spin}^c$-Bordism and a Twisted Anomaly Map

    math.AT 2025-10 conditional novelty 8.0 of 10

    Differential models for twisted Spin^c-bordism and its Anderson dual are constructed, together with a twisted anomaly map from differential twisted K-theory.

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