Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory
Abstract
We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2013
- DOI:
- 10.48550/arXiv.1306.0247
- arXiv:
- arXiv:1306.0247
- Bibcode:
- 2013arXiv1306.0247B
- Keywords:
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- Mathematics - K-Theory and Homology;
- Mathematics - Algebraic Topology;
- Mathematics - Differential Geometry;
- 19E20
- E-Print:
- 198 pages (thoroughly revised version)