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.
univienna.zoom.us/j/63166383248