Differential Arithmetic Geometry (A02)

Subject Area Mathematics
Term from 2014 to 2021
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 224262486
 

Project Description

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
Subproject of SFB 1085:  Higher Invariants – Interactions between Arithmetic Geometry and Global Analysis
Applicant Institution Universität Regensburg
Project Heads Professor Dr. Ulrich Bunke; Professor Dr. Guido Kings; Dr. Georgios Raptis; Dr. Georg Tamme