Odd primary equivariant rigidity and equivariant derivators

• Applicant: Professor Dr. Stefan Schwede
• Subject Area: Mathematics
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 269314998

Homotopy theory is an area of pure mathematics that investigates those aspects of geometric objects that are invariant under continuous deformations. Homotopy theory lies at the interface between the world of continuous and smooth objects (geometry and analysis) and the discrete world (algebra and combinatorics). Characteristic for equivariant homotopy theory is the additional presence of symmetries that must be preserved by all deformations. Typical questions are the classification of geometric objects of a certain kind with specified symmetry, or of the maps between them.This project does not study individual equivariant geometric objects, but rather the fundamental properties of the collection of all topological objects with a specified finite symmetry. The primary goal is the proof of a rigidity theorem, namely that all higher order homotopy theoretic properties are already determined by the first order approximation (the homotopy category).

• DFG Programme: Priority Programmes
• Subproject of: SPP 1786: Homotopy Theory and Algebraic Geometry