Text only print
Full screen print
Tuesday Seminar on Topology
Seminar information archive ～04/06｜Next seminar｜Future seminars 04/07～
| Date, time & place | Tuesday 16:00 - 17:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | IKE Yuichi, KONNO Hokuto, SAKASAI Takuya |
2026/04/28
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Taketo Sano (RIKEN)
A y-ification of Khovanov homology (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Taketo Sano (RIKEN)
A y-ification of Khovanov homology (JAPANESE)
[ Abstract ]
In this talk, I will explain the main results of my recent paper (arXiv:2602.17435).
Khovanov homology is a categorification of the Jones polynomial, introduced by M. Khovanov. A persistent theme in the subject is that adding extra structures on Khovanov homology strengthens the invariant, and often detects phenomena invisible at the level of polynomials or bigraded vector spaces.
Motivated by the y-ification of HOMFLY--PT homology by Gorsky and Hogancamp, and the sl2-action constructed by Gorsky, Hogancamp and Mellit, we construct a y-ification of Khovanov homology and define an action of the element e in sl2 on these y-ifications. Our construction is compatible with the previous ones via Rasmussen's spectral sequence from HOMFLY--PT homology to Khovanov homology; yet our approach is more elementary and suited to diagrammatic and algorithmic computations. As an application, we show that the additional structure can distinguish knots with identical Khovanov homology and identical HOMFLY--PT homology, in particular the Conway knot and the Kinoshita--Terasaka knot.
[ Reference URL ]In this talk, I will explain the main results of my recent paper (arXiv:2602.17435).
Khovanov homology is a categorification of the Jones polynomial, introduced by M. Khovanov. A persistent theme in the subject is that adding extra structures on Khovanov homology strengthens the invariant, and often detects phenomena invisible at the level of polynomials or bigraded vector spaces.
Motivated by the y-ification of HOMFLY--PT homology by Gorsky and Hogancamp, and the sl2-action constructed by Gorsky, Hogancamp and Mellit, we construct a y-ification of Khovanov homology and define an action of the element e in sl2 on these y-ifications. Our construction is compatible with the previous ones via Rasmussen's spectral sequence from HOMFLY--PT homology to Khovanov homology; yet our approach is more elementary and suited to diagrammatic and algorithmic computations. As an application, we show that the additional structure can distinguish knots with identical Khovanov homology and identical HOMFLY--PT homology, in particular the Conway knot and the Kinoshita--Terasaka knot.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
