Dimitri Ara (Université Paris 7), On Grothendieck infinity-groupoids


  • March 1, 2012, 17:30 - 18:30


In Pursuing Stacks, Grothendieck defines a notion of (weak) ∞-groupoid and constructs a fundamental ∞-groupoid functor that associates to every topological space its fundamental ∞-groupoid. He conjectures that this functor induces an equivalence on the homotopy categories, and in particular that ∞-groupoids classify homotopy types. In this talk, we will explain Grothendieck's definition and we will give a precise statement of Grothendieck's conjecture. If time allows, we will study the homotopy theory of Grothendieck ∞-groupoids.