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AG Seminar 10.02.2022 - Sylvain Douteau

Homotopy links and stratified homotopy theories

The study of stratified spaces and their invariants was first motivated by Whitney's theorem, stating that any real or complex algebraic variety can be decomposed into strata that are smooth varieties satisfying gluing conditions. This led to numerous extension of invariants from manifold to pseudo-manifold - those objects that Whitney defined - such as intersection cohomology or the exit-path infinity category. Those extended invariant are only invariant under stratum preserving homotopies, which motivates the study of an appropriate homotopy theory of stratified spaces.

In this talk, I will present two independant - and a priori non-equivalent - ways of producing such a stratified homotopy theory. I will explain how the study of suitable generalization of Quinn's homotopy links allow for a comparison between these two point of views.

This talk will be based in part on work in common with Lukas Waas (Heidelberg University)