Sylvain Douteau: Postdoc day, Seminar 2: An illustration of stratified homotopy theory

Abstract: The theory of stratified spaces was motivated by the study of singular objects, through decompositions into smooth pieces, following the famous decomposition theorem by Whitney. In this context, stratified homotopy theory is an adaptation of the usual homotopy theory of spaces, suited for the study of the invariants of those singular objects. However, one can also use stratifications to encode particular structures on spaces. In this case, the stratified homotopy type of the space becomes an invariant of the structure. We will illustrate this phenomenon through an application to knot theory.