Definable refinements of algebraic invariants

24.11.2022 10:00 - 10:45

Martino Lupini (Newcastle University)

Abstract: I will give an overview of the framework of “Borel-definable” homological algebra and algebraic topology that I have recently developed in collaboration with Bergfalk and Panagiotopoulos. In this context, classical invariants from algebra, analysis, and topology, such as Čech cohomology, Steenrod homology, bounded cohomology, and K-homology, are enriched with additional structure that allows one to keep track of additional topological and complexity-theoretic information. This yields stronger invariants that are finer, richer, and more rigid than their classical counterparts. I will then present several applications of this viewpoint to topology and homotopy theory, commutative algebra, operator algebras, and group theory.




Fakultät für Mathematik, Dekan R. I. Bot
SR 06, 1. OG, OMP 1