Sylvain Douteau: Stratified homotopy theory
Time: Tue 2020-11-17 11.15 - 12.00
Location: Zoom, meeting ID: 657 9019 8929
Participating: Sylvain Douteau, Université de Picardie Jules Verne
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.