Séminaires : Séminaire de Topologie

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) Olga Plamenevskaya - Stony Brook University,
Titre [K-OS] Unexpected Stein fillings, rational surface singularities, and line arrangements
Date27/01/2022
Horaire14:00 à 15:00
Diffusion https://lrobert.perso.math.cnrs.fr/join-kos.html
RésumeA link of an isolated complex surface singularity is a 3-manifold obtained by intersecting the surface with a small sphere centered at the singular point. The link carries a canonical contact structure, given by the complex tangencies. Milnor fibers of possible smoothings of the singular point give Stein fillings for this contact structure; deformations of the singularity give rise to Stein cobordisms between the corresponding links. This leads to many interesting questions regarding the interplay of algebraic geometry, topology, and symplectic geometry.
After setting the stage, we will focus on the following question: do Milnor fibers and the resolution of a surface singularity yield ALL possible Stein fillings of its link? This is known to hold in some simple cases, eg for lens spaces. We show that even in the "next simplest" case, for many rational singularities, there is a plethora of "unexpected" Stein fillings that do not arise from Milnor fibers of any smoothings. To compare fillings and smoothings, we use T.de Jong-D.van Straten's description of Milnor fibers of certain rational surface singularities in terms of deformations of associated singular plane curves. On the symplectic side, we develop an analogous description of the Stein fillings via certain more general arrangements of curves. "Unexpected" arrangements then give rise to "unexpected" fillings. (Joint work with L. Starkston.)
All the discussion will be from the topological perspective, with minimal input from algebraic geometry.
Salle1016
AdresseSophie Germain
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