A geometric model for odd differential K-theory |
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Institution: | 1. School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia;2. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland |
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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 16], which states that the model developed there also defines the unique differential extension of odd K-theory. |
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Keywords: | 19L50 19L10 22E67 57R19 57R20 81T30 |
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