A differential extension of a generalized cohomology theory combines topological information about cohomology classes on manifolds with differential form data. The Transfer-Index-Conjecture compares an analytic and a topological push-forward along a proper submersion of manifolds in differential algebraic K-theory of a number ring. It contains known index theorems of Dwyer-Weiss-Williams and of Bismut-Lott. The main goal of the project is to prove this conjecture. Moreover, we will study arithmetic consequences and generalizations.
DFG Programme
Collaborative Research Centres
