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An elementary differential extension of odd K-theory

Published online by Cambridge University Press:  04 April 2013

Thomas Tradler ,
Scott O. Wilson  and
Mahmoud Zeinalian
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Abstract

There is an equivalence relation on the set of smooth maps of a manifold into the stable unitary group, defined using a Chern-Simons type form, whose equivalence classes form an abelian group under ordinary block sum of matrices. This construction is functorial, and defines a differential extension of odd K-theory, fitting into natural commutative diagrams and exact sequences involving K-theory and differential forms. To prove this we obtain along the way several results concerning even and odd Chern and Chern-Simons forms.

Keywords

K-theorydifferential K-theoryChern-Simons19L5058J2819E20
Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 2 , October 2013 , pp. 331 - 361
Copyright
Copyright © ISOPP 2013 

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