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arXiv · 1309.2834

A Geometric Model for Odd Differential K-theory

Pedram Hekmati·Michael K. Murray·Vincent S. Schlegel·Raymond F. Vozzo
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Abstract

Odd $K$-theory has the interesting property that it admits an infinite number of inequivalent differential refinements. In this paper we provide a bundle theoretic model for odd differential $K$-theory using the caloron correspondence and prove that this refinement is unique up to a unique natural isomorphism. We characterise the odd Chern character and its transgression form in terms of a connection and Higgs field and discuss some applications. Our model can be seen as the odd counterpart to the Simons-Sullivan construction of even differential $K$-theory. We use this model to prove a conjecture of Tradler-Wilson-Zeinalian regarding a related differential extension of odd $K$-theory

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Pedram Hekmati, Michael K. Murray, Vincent S. Schlegel, Raymond F. Vozzo. 2015-03-16. A Geometric Model for Odd Differential K-theory. https://doi.org/10.1016/j.difgeo.2015.02.001

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