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arXiv · 1211.4477

An Elementary Differential Extension of Odd K-theory

Thomas Tradler·Scott O. Wilson·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.

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Thomas Tradler, Scott O. Wilson, Mahmoud Zeinalian. 2012-11-19. An Elementary Differential Extension of Odd K-theory. https://arxiv.org/abs/1211.4477

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