Sylvain Douteau: Stratified homotopy theory

Abstract

Stratified spaces appear naturally in singularity theory. In the 80's, Goresky and MacPherson introduced intersection cohomology to generalize the cohomological properties of manifolds to some well-behaved stratified objects : the pseudo-manifolds. But intersection cohomology is not compatible with classical homotopy theory. This motivates the development of a new homotopy theory, better suited for the study of stratified spaces. In this talk, after giving a quick review of some classical results in homotopy theory that we intend to generalise, I will present two approaches to the problem of constructing a stratified homotopy theory : one simplicial, and one topological. We will explain how these two compare to each other and to the standard case, and present a new invariant of stratified spaces : the stratified homotopy groups.

Zoom Notes: The meeting ID is 657 9019 8929 and the passcode is 3517257.