Groupes de travail : Cohomology of Torelli groups

Equipe(s) Responsable(s)SalleAdresse
Topologie et Géométrie Algébrique
Erik Lindell, Najib Idrissi
1013 Sophie Germain

The overall goal of the working group is to understand the following paper:

[2307.07082] The second rational homology of the Torelli group is finitely generated (arxiv.org) by Daniel Minahan

For handwritten notes taken during the talks by Najib, see this page.

Séances à suivre

Orateur(s)Titre Date DébutSalleAdresseDiffusion
+ Adrien Brochier The Johnson homomorphism 28/02/2024 14:00 1016 Sophie Germain
+ TBA 06/03/2024 14:00 1016 Sophie Germain
+ TBA (salle inhabituelle !) 13/03/2024 14:00 6033 Sophie Germain
+ Séances antérieures

Séances antérieures

Orateur(s)Titre Date DébutSalleAdresse
+ Adrien Brochier The Johnson homomorphism 14/02/2024 14:00 1016 Sophie Germain
+ Marie-Camille Delarue Erik Lindell Transvective representations 07/02/2024 14:00 1016 Sophie Germain
+ Jules Martel Muriel Livernet Curve complexes and C_[a](S) 31/01/2024 14:00 1016 Sophie Germain
+ Juan Ramon Gomez Garcia Emmanuel Wagner Spectral sequences 24/01/2024 14:00 1016 Sophie Germain
+ Juan Ramon Gomez Garcia Emmanuel Wagner Spectral sequences 17/01/2024 09:15 1013 Sophie Germain
+ Clovis Chabertier Najib Idrissi Group homology and cohomology 13/12/2023 09:15 1013 Sophie Germain
+ Laura Marino Jules Martel More background on Mod(S) and I(S) (2/2) 06/12/2023 09:15 1013 Sophie Germain
+ Laura Marino Jules Martel More background on Mod(S) and I(S) (1/2) 29/11/2023 09:15 1013 Sophie Germain
+ Erik Lindell Introduction to the working group 08/11/2023 09:15 1013 Sophie Germain

The mapping class groups of a (compact, orientable) surface is the group of isotopy classes of orientation-preserving self-diffeomorphisms of the surface. This group is an object of fundamental interest in low-dimensional topology, which also has important connections to several other areas, such as algebraic and hyperbolic geometry. The Torelli group of a surface is the subgroup of the mapping class group consisting of those elements which act trivially on the homology of the surface (this can be thought of as the "non-linear" part of the group). In comparison to mapping class groups, we know very little about Torelli groups, even when it comes to basic group theoretic properties, such as whether they are finitely presentable. A recent result of Minahan states that for surfaces of sufficiently large genus, the second rational cohomology of the Torelli group is finite dimensional, which rules out the simplest obstruction to finite presentability. The goal of this working group will be to understand this result of Minahan, and learn about cohomology of Torelli groups, and the methods used to study it, more generally. In this first talk, I will give a gentle introduction to mapping class groups and Torelli groups and survey some of what we know about their (rational) cohomology, without assuming any prior knowledge of the subject. 

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