Ressource pédagogique : J. Fine - Knots, minimal surfaces and J-holomorphic curves

cours / présentation - Date de création : 02-07-2021
Auteur(s) : Jöel FINE
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Présentation de: J. Fine - Knots, minimal surfaces and J-holomorphic curves

Informations pratiques sur cette ressource

Langue du document : Anglais
Type pédagogique : cours / présentation
Niveau : doctorat
Durée d'exécution : 1 heure 1 minute 3 secondes
Contenu : image en mouvement
Document : video/mp4
Taille : 1.06 Go
Droits d'auteur : libre de droits, gratuit
Droits réservés à l'éditeur et aux auteurs. CC BY-NC-ND 4.0

Description de la ressource pédagogique

Description (résumé)

I will describe work in progress, parts of which are joint with Marcelo Alves. Let L be a knot or link in the 3-sphere. I will explain how one can count minimal surfaces in hyperbolic 4-space which have ideal boundary equal to L, and in this way obtain a knot invariant. In other words the number of minimal surfaces doesn’t depend on the isotopy class of the link. These counts of minimal surfaces can be organised into a two-variable polynomial which is perhaps a known polynomial invariant of the link, such as HOMFLYPT. “Counting minimal surfaces” needs to be interpreted carefully here, similar to how Gromov-Witten invariants “count” J-holomorphic curves. Indeed I will explain how this “minimal surface polynomial" can be seen as a Gromov-Witten invariant for the twistor space of hyperbolic 4-space. This leads naturally to a new class of infinite-volume 6-dimensional symplectic manifolds with well behaved counts of J-holomorphic curves. This gives more potential knot invariants, for knots in 3-manifolds other than the 3-sphere. It also enables the counting of minimal surfaces in more general Riemannian 4-manifolds, besides hyperbolic space.

"Domaine(s)" et indice(s) Dewey

  • Mathématiques (510)

Thème(s)

Intervenants, édition et diffusion

Intervenants

Fournisseur(s) de contenus : Fanny Bastien, Hugo BÉCHET

Diffusion

Document(s) annexe(s) - J. Fine - Knots, minimal surfaces and J-holomorphic curves

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AUTEUR(S)

  • Jöel FINE

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  • Identifiant de la fiche
    63113
  • Identifiant
    oai:canal-u.fr:63113
  • Schéma de la métadonnée
  • Entrepôt d'origine
    Canal-U