Dimitri Ara (Université Paris 7), On Grothendieck infinity-groupoids
Schedule
- March 1, 2012, 17:30 - 18:30
Abstract
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.
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.