Differential function spectra, the differential BeckerGottlieb transfer, and applications to differential algebraic Ktheory
Abstract
We develop differential algebraic Ktheory 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 Ktheory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential BeckerGottlieb transfer. We then state a transfer index conjecture about the equality of the BeckerGottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some nontrivial consequences which are provable by independent means.
 Publication:

arXiv eprints
 Pub Date:
 June 2013
 arXiv:
 arXiv:1306.0247
 Bibcode:
 2013arXiv1306.0247B
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Algebraic Topology;
 Mathematics  Differential Geometry;
 19E20
 EPrint:
 198 pages (thoroughly revised version)