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Bridge trisections of knotted surfaces in four-manifolds
Post-edited
Authors : Meier, Jeffrey (Author of the conference)
CIRM (Publisher )
57M25 - Knots and links in $S^3$
57M50 - Geometric structures on low-dimensional manifolds
57Q45 - Knots and links in high dimensions (PL-topology)
CIRM (Publisher )
Abstract :
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
MSC Codes : 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
57M25 - Knots and links in $S^3$
57M50 - Geometric structures on low-dimensional manifolds
57Q45 - Knots and links in high dimensions (PL-topology)
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 20/02/2018 Conference Date : 13/02/2018 Subseries : Research talks arXiv category : Geometric Topology Mathematical Area(s) : Topology ; Geometry Format : MP4 (.mp4) - HD Video Time : 01:04:38 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-02-13_Meier.mp4 
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Information on the Event
Event Title : Knotted embeddings in dimensions 3 and 4 / Plongements noués en dimension 3 et 4Event Organizers : Audoux, Benjamin ; Baader, Sebastian ; Lecuona, Ana G. Dates : 12/02/2018 - 16/02/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1893.html
Citation Data
DOI : 10.24350/CIRM.V.19357903Cite 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 |
See Also
- [Multi angle] Quantum $\mathfrak{sl}_n$ knot cohomology and the slice genus / Author of the conference Lobb, Andrew.
- [Multi angle] Covering spaces and spanning trees / Author of the conference Cimasoni, David.
- [Multi angle] Trisections diagrams and surgery operations on embedded surfaces / Author of the conference Gay, David.
- [Multi angle] Surface systems for links / Author of the conference Powell, Mark.
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.
- Meier, J. (2017). Trisections and spun 4-manifolds.
- 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
