Knotted embeddings in dimensions 3 and 4 / Plongements noués en dimension 3 et 4

Collection Knotted embeddings in dimensions 3 and 4 / Plongements noués en dimension 3 et 4

Organizer(s) Audoux, Benjamin ; Baader, Sebastian ; Lecuona, Ana G.

Date(s) 12/02/2018 - 16/02/2018

linked URL https://conferences.cirm-math.fr/1893.html

00:00:00 / 00:00:00

2 5

Chapters

Bridge trisections of knotted surfaces in four-manifolds

By Jeffrey Meier

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.

Information about the video

Date of recording 13/02/2018
Date of publication 20/02/2018
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19357903
Cite this video Meier, Jeffrey (13/02/2018). Bridge trisections of knotted surfaces in four-manifolds. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19357903
URL https://dx.doi.org/10.24350/CIRM.V.19357903

Domain(s)

Geometric Topology

Bibliography

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. <arXiv:1710.01745> - https://arxiv.org/abs/1710.01745
Meier, J. (2017). Trisections and spun 4-manifolds. <arXiv:1708.01214> - 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

MSC codes

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All the collection videos

01:03:10

published on February 18, 2018

Trisections diagrams and surgery operations on embedded surfaces

By David Gay

01:04:38

published on February 20, 2018

Bridge trisections of knotted surfaces in four-manifolds

By Jeffrey Meier

01:03:30

published on February 18, 2018

Surface systems for links

By Mark Powell

01:02:31

published on February 18, 2018

Covering spaces and spanning trees

By David Cimasoni

$Quantum $\mathfrak{sl}_n$ knot cohomology and the slice genus$
50:00

published on February 19, 2018

Quantum $\mathfrak{sl}_n$ knot cohomology and the slice genus

By Andrew Lobb

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