| Equipe(s) : | tga, |
| Responsables : | Catherine Gille et Najib Idrissi |
| Email des responsables : | |
| Salle : | 1016 |
| Adresse : | Sophie Germain |
| Description | Un plan d’accès est disponible ici. Pour vous inscrire à la liste de diffusion du séminaire, veuillez vous rendre à cette adresse. Le séminaire de topologie évolue. Des après-midi de topologie seront organisées tout au long de l'année (en collaboration avec USPN) et nous vous en tiendrons informé(e)s sur cette liste de diffusion. |
| Orateur(s) | Quentin Faes - Université de Bourgogne, |
| Titre | [K-OS] Triviality of the J_4-equivalence among homology 3-spheres |
| Date | 07/04/2022 |
| Horaire | 14:00 à 15:00 |
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| Diffusion | https://lrobert.perso.math.cnrs.fr/join-kos.html |
| Résume | Redemeister–Singer theorem states that, up to homeomorphism, any compact connected oriented 3-manifold can be obtained by gluing two handlebodies together. This connects the study of 3-manifolds to the study of the mapping class group of surfaces. For instance, one can get all homology 3-spheres by restricting the gluing map to be an element acting trivially on the homology of the surface, i.e. an element of the Torelli group. Another point of view is to say that one can get any homology 3-sphere from 𝕊3 by performing the following surgery : remove a handlebody and glue it back with an element of the Torelli group. Somewhat surprisingly, we shall prove in this talk that we can actually suppose this surgery to be performed with an element of the 4-th term of the Johnson filtration, i.e. an element acting trivially on the 4-th nilpotent quotient of the fundamental group of the surface. This result is an improvement of results obtained successively by Morita and Pitsch. It is obtained by using Goussarov–Habiro clasper calculus, a formula by Morita computing the Casson invariant of homology 3-spheres, and a formula by Kawazumi and Kuno that encodes the action of a Dehn twist on the fundamental group. |
| Salle | 1016 |
| Adresse | Sophie Germain |