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Tuesday Seminar on Topology
Seminar information archive ～05/27｜Next seminar｜Future seminars 05/28～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | HABIRO Kazuo, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2025/06/17
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Taketo Sano (RIKEN iTHEMS)
A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Taketo Sano (RIKEN iTHEMS)
A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms (JAPANESE)
[ Abstract ]
Rasmussen's s-invariant is an integer-valued knot invariant derived from Khovanov homology, and it has remarkable applications in topology, such as providing a combinatorial reproof of the Milnor conjecture. Although the s-invariant is defined using the quantum filtration of the homology group, it is difficult to interpret it geometrically. In this talk, we give a cobordism-based interpretation of the s-invariant based on Bar-Natan’s reformulation of Khovanov homology via tangles and cobordisms. This interpretation allows for the computation of the s-invariant from a tangle decomposition of the knot. As an application, we demonstrate that the s-invariants of a certain infinite family of pretzel knots can be determined by hand.
[ Reference URL ]Rasmussen's s-invariant is an integer-valued knot invariant derived from Khovanov homology, and it has remarkable applications in topology, such as providing a combinatorial reproof of the Milnor conjecture. Although the s-invariant is defined using the quantum filtration of the homology group, it is difficult to interpret it geometrically. In this talk, we give a cobordism-based interpretation of the s-invariant based on Bar-Natan’s reformulation of Khovanov homology via tangles and cobordisms. This interpretation allows for the computation of the s-invariant from a tangle decomposition of the knot. As an application, we demonstrate that the s-invariants of a certain infinite family of pretzel knots can be determined by hand.
Preprint: https://arxiv.org/abs/2503.05414
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
