CIRM - Videos & books Library - Bridge trisections of knotted surfaces in four-manifolds

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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

Réalisateur :

Hennenfent, Guillaume

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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

Données de citation

DOI : 10.24350/CIRM.V.19357903
Citer cette vidéo: 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

Voir aussi

[Multi angle] Quantum $\mathfrak{sl}_n$ knot cohomology and the slice genus / Auteur de la Conférence Lobb, Andrew.
[Multi angle] Covering spaces and spanning trees / Auteur de la Conférence Cimasoni, David.
[Multi angle] Trisections diagrams and surgery operations on embedded surfaces / Auteur de la Conférence Gay, David.
[Multi angle] Surface systems for links / Auteur de la Conférence Powell, Mark.

Bibliographie

Gay, D.T., & Kirby, R. (2016). Trisecting 4-manifolds. Geometry & Topology, 20(6), 3097-3132 - https://doi.org/10.2140/gt.2016.20.3097

Meier, J., & Zupan, A. (2017). Bridge trisections of knotted surfaces in 4-manifolds. - https://arxiv.org/abs/1710.01745

Meier, J. (2017). Trisections and spun 4-manifolds. - https://arxiv.org/abs/1708.01214

Meier, J., & Zupan, A. (2017). Bridge trisections of knotted surfaces in $S^4$. Transactions of the American Mathematical Society, 369(10), 7343-7386 - https://doi.org/10.1090/tran/6934

Meier, J., & Zupan, A. (2017). Genus-two trisections are standard. Geometry & Topology, 21(3), 1583-1630 - https://doi.org/10.2140/gt.2017.21.1583

Meier, J., Schirmer, T., & Zupan, A. (2016). Classification of trisections and the Generalized Property R Conjecture. Proceedings of the American Mathematical Society, 144(11), 4983-4997 - https://doi.org/10.1090/proc/13105

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