Stratified homotopy theory

Clark Barwick (University of Edinburgh)

Monday 28th October 16:00-17:00 Maths 311B

Abstract

Homotopy invariants of topological spaces can be understood systematically by working with certain combinatorial models of their homotopy types called ‘higher groupoids’; this is essentially a beautiful insight of Dan Kan in the 1950s. A couple years ago, I suggested that, analogously, homotopy invariants of stratified topological spaces should be understood systematically by working with certain combinatorial models of their homotopy types called ‘higher categories’. Last month, a tour-de-force work of Peter Haine finally proved that claim. I shall tell this story and share some details of both the intuition behind this and Haine’s proof.

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