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H 2 Bridge trisections of knotted surfaces in four-manifolds​

Auteurs : Meier, Jeffrey (Auteur de la Conférence)
CIRM (Editeur )

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trisections of 4-manifolds trisection diagrams bridge trisections trivial tangles knotted surfaces in $S^4$ tri-plane diagrams complex curves and surfaces shadow diagrams shadow diagrams for curves in $\mathbb{CP}^2$ questions from the audience

Résumé : In this talk, we will develop the theory of generalized bridge trisections for smoothly embedded closed surfaces in smooth, closed four-manifolds. The main result is that any such surface can be isotoped to lie in bridge trisected position with respect to a given trisection of the ambient four-manifold. In the setting of knotted surfaces in the four-sphere, this gives a diagrammatic calculus that offers a promising new approach to four-dimensional knot theory. However, the theory extends to other ambient four-manifolds, and we will pay particular attention to the setting of complex curves in simple complex surfaces, where the theory produces surprisingly satisfying pictures and leads to interesting results about trisections of complex surfaces.
This talk is based on various joint works with Dave Gay, Peter Lambert-Cole, and Alex Zupan.

Keywords : bridge trisections; bridge splittings; trisections of 4-manifolds; 4-dimensional knot theory; trisections of complex surfaces; knotted surfaces; 4-sphere; Heegaard splittings

Codes MSC :
57M25 - Knots and links in $S^3$
57M50 - Geometric structures on low-dimensional manifolds
57Q45 - Knots and links in high dimensions (PL-topology)

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 20/02/2018
    Date de captation : 13/02/2018
    Collection : Research talks ; Geometry ; Topology
    Format : MP4 (.mp4) - HD
    Durée : 01:04:38
    Domaine : Topology ; Geometry
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2018-02-13_Meier.mp4

Informations sur la rencontre

Nom de la rencontre : Knotted embeddings in dimensions 3 and 4 / Plongements noués en dimension 3 et 4
Organisateurs de la rencontre : Audoux, Benjamin ; Baader, Sebastian ; Lecuona, Ana G.
Dates : 12/02/2018 - 16/02/2018
Année de la rencontre : 2018
URL Congrès : https://conferences.cirm-math.fr/1893.html

Citation Data

DOI : 10.24350/CIRM.V.19357903
Cite this video as: Meier, Jeffrey (2018). Bridge trisections of knotted surfaces in four-manifolds​. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19357903
URI : http://dx.doi.org/10.24350/CIRM.V.19357903

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