Jean Morlet Chair - Trisections and related topics / Chaire Jean Morlet - Trisections et interactions

Collection Jean Morlet Chair - Trisections and related topics / Chaire Jean Morlet - Trisections et interactions

Organizer(s) Gay, David ; Moussard, Delphine

Date(s) 13/10/2025 - 17/10/2025

linked URL https://conferences.cirm-math.fr/3298.html

00:00:00 / 00:00:00

2 4

Cornered skein lasagna theory

By Sarah Blackwell

The theory of skein lasagna modules, initiated by Morrison-Walker-Wedrich, has been the subject of much interest in recent years. This theory takes as input Khovanov-Rozansky link homology and yields invariants of oriented 4-manifolds, which are generally very powerful yet hard to calculate. Most excitingly, this theory was used recently to detect exotic compact 4-manifolds by Ren-Willis, marking the first such result proven without the use of gauge theory. In this talk I will discuss an extension of skein lasagna theory for cornered 4-manifolds and describe an application to trisections of 4-manifolds, with an eye towards calculations. This is joint work with Slava Krushkal and Yangxiao Luo.

Information about the video

Date of recording 14/10/2025
Date of publication 30/10/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20395003
Cite this video Blackwell, Sarah (14/10/2025). Cornered skein lasagna theory. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20395003
URL https://dx.doi.org/10.24350/CIRM.V.20395003

Domain(s)

Geometric Topology

Bibliography

GAY, David et KIRBY, Robion. Trisecting 4–manifolds. Geometry & Topology, 2016, vol. 20, no 6, p. 3097-3132. - https://doi.org/10.2140/gt.2016.20.3097
MANOLESCU, Ciprian et NEITHALATH, Ikshu. Skein lasagna modules for 2-handlebodies. Journal für die reine und angewandte Mathematik (Crelles Journal), 2022, vol. 2022, no 788, p. 37-76. - https://doi.org/10.1515/crelle-2022-0021
MANOLESCU, Ciprian, WALKER, Kevin, et WEDRICH, Paul. Skein lasagna modules and handle decompositions. Advances in Mathematics, 2023, vol. 425, p. 109071. - https://doi.org/10.1016/j.aim.2023.109071
MORRISON, Scott, WALKER, Kevin, et WEDRICH, Paul. Invariants of 4-manifolds from Khovanov-Rozansky link homology. Geom. Topol, 2022, vol. 26, no 8, p. 3367-3420. - http://dx.doi.org/10.2140/gt.2022.26.3367
REN, Qiuyu et WILLIS, Michael. Khovanov homology and exotic $4 $-manifolds. arXiv preprint arXiv:2402.10452, 2024. - https://doi.org/10.48550/arXiv.2402.10452
SULLIVAN, Ian A. et ZHANG, Melissa. Kirby belts, categorified projectors, and the skein lasagna module of s2× S2. arXiv preprint arXiv:2402.01081, 2024. - https://doi.org/10.48550/arXiv.2402.01081

MSC codes

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