Differential Function Spectra The Differential Becker Gottlieb Transfer And Applications To Differential Algebraic K Theory

Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic K-theory

Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic K-Theory

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.

Differential Characters

Providing a systematic introduction to differential characters as introduced by Cheeger and Simons, this text describes important concepts such as fiber integration, higher dimensional holonomy, transgression, and the product structure in a geometric manner. Differential characters form a model of what is nowadays called differential cohomology, which is the mathematical structure behind the higher gauge theories in physics.