Homological algebra for stable ∞-categories (C02)

• Subject Area: Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 427320536

The general goal of the project is to study the homological algebra of stable infinity-categories and Poincaré infinity-categories. This is done through the theory of non-commutative motives and Efimov K-Theory. Concrete goals are to give a new approach to controlled algebra (thereby attacking open problems and conjectures in geometric topology) and obtain new structural results about the category of motives. The latter thus yields new results about K-Theory and TC, e.g. we try to resolve the long-standing open question about a universal property for TC.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1442: Geometry: Deformations and Rigidity
• Applicant Institution: Universität Münster
• Project Head: Professor Dr. Thomas Nikolaus