Differential Arithmetic Geometry (A02)

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

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