Automorphisms of procongruence mapping class groups
Marco Boggi (UFMG Belo Horizonte)
Abstract: In this talk, I will discuss the automorphism group of the procongruence mapping class group and of the associated procongruence curve and pants complexes. In analogy with a classical result of Ivanov for mapping class groups, this allows to determine the group of automorphisms of the $arithmetic$ procongruence mapping class group which satisfy a natural geometric condition. It is a nontrivial fact that this condition holds in genus $0$. Let $\mathcal{M}_{0,n}$ be the moduli space of $n$-labeled, genus $0$ algebraic curves. It follows, in particular, that $\mathrm{Out}(\pi_1^\mathrm{et}(\mathcal{M}_{0,n}\otimes\Q))\cong\Sigma_n$ for $n\geq 5.\newline$ This talk is based on a joint work with Louis Funar and Pierre Lochak (cf. $\texttt{arXiv:2004.04135}$).
algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologymetric geometryquantum algebrarepresentation theory
Audience: researchers in the topic
Series comments: Weekly research seminar in algebra and geometry.
"Sapienza" Università di Roma, Department of Mathematics "Guido Castelnuovo".
Organizers: | Simone Diverio*, Guido Pezzini* |
*contact for this listing |