Monday 28 February 2022
15:00–16:30*

Jacques Darné (UCLouvain) — Filtrations on the Mapping Class Group of the punctured sphere

The Mapping Class Group of the n-punctured sphere (fixing a basepoint) classically identifies with the quotient B_n^* of the Artin braid group by its center. This group acts faithfully on the fundamental group of the the n-punctured sphere, which is free on n-1 generators. From this action, one can define a filtration of B_n^* by subgroups B_n^* ⊇ A₁ ⊇ A₂ ⊇ ⋯, which are the analogues of the Johnson kernels in this situation. It turns out that this filtration is exactly the lower central series of the corresponding pure mapping class group P_n^*, and that we understand fairly well the associated Lie algebra, using Milnor invariants adapted to these mapping classes. In this talk, I intend to explain these results, and to give you a taste of the techniques involved in their proofs.

* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.