Stable homotopy theory for topological algebras

• Applicant: Professor Dr. Ulrich Bunke
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 567014451

The goal of the project is the construction of a universal homological functor for topological algebras. The model is the construction of an infinity-categorical enhancement of KK-theory for C*-algebras. The notion of a topological algebra will be understood in a broad sense and will encompass group actions, parametrization over manifolds and analytic structures in the sense of condensed mathematics. As a more advanced goal we want to understand the relation between the theory to be constructed and the theory of non-commutative motives.

• DFG Programme: Research Grants