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Tuesday Seminar on Topology
Seminar information archive ～04/03｜Next seminar｜Future seminars 04/04～
| Date, time & place | Tuesday 16:00 - 17:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | IKE Yuichi, KONNO Hokuto, SAKASAI Takuya |
Future seminars
2026/04/07
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Tatsumasa Suzuki (The University of Tokyo)
Price twist and pochette surgery constructing non-simply connected closed 4-manifolds (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tatsumasa Suzuki (The University of Tokyo)
Price twist and pochette surgery constructing non-simply connected closed 4-manifolds (JAPANESE)
[ Abstract ]
A cut-and-paste operation along an embedded real projective plane in a 4-manifold is called a Price twist. A Price twist on the 4-sphere produces, up to diffeomorphism, at most three 4-manifolds: the 4-sphere itself, a homotopy 4-sphere, and a non-simply connected closed 4-manifold. In general, the classification of diffeomorphism types of non-simply connected closed 4-manifolds is still far from being well understood. In this talk, we focus on Price twists on the 4-sphere associated with embeddings of the real projective plane of Kinoshita type that yield non-simply connected 4-manifolds. We present several properties of these manifolds and results on the classification of their diffeomorphism types. We also explain pochette surgery, introduced by Zjuñici Iwase and Yukio Matsumoto, which is closely related to the results of this work. This talk is based on joint work with Tsukasa Isoshima (Keio University).
[ Reference URL ]A cut-and-paste operation along an embedded real projective plane in a 4-manifold is called a Price twist. A Price twist on the 4-sphere produces, up to diffeomorphism, at most three 4-manifolds: the 4-sphere itself, a homotopy 4-sphere, and a non-simply connected closed 4-manifold. In general, the classification of diffeomorphism types of non-simply connected closed 4-manifolds is still far from being well understood. In this talk, we focus on Price twists on the 4-sphere associated with embeddings of the real projective plane of Kinoshita type that yield non-simply connected 4-manifolds. We present several properties of these manifolds and results on the classification of their diffeomorphism types. We also explain pochette surgery, introduced by Zjuñici Iwase and Yukio Matsumoto, which is closely related to the results of this work. This talk is based on joint work with Tsukasa Isoshima (Keio University).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/04/14
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Yukihiro Okamoto (Tokyo Metropolitan University)
Non-contractible loops of Legendrian tori from families of knots (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yukihiro Okamoto (Tokyo Metropolitan University)
Non-contractible loops of Legendrian tori from families of knots (JAPANESE)
[ Abstract ]
The unit cotangent bundle of the Euclidean space R3 has a canonical contact structure. In this talk, we discuss loops of Legendrian tori in this 5-dimensional contact manifold. In particular, we focus on loops arising as families of the unit conormal bundles of knots in R3, and I will explain a topological method to compute the monodromy on the Legendrian contact homology in degree 0 induced by those loops. As an application, we get examples of non-contractible loops of Legendrian tori which are contractible in the space of smoothly embedded tori. This is joint work with Marián Poppr.
[ Reference URL ]The unit cotangent bundle of the Euclidean space R3 has a canonical contact structure. In this talk, we discuss loops of Legendrian tori in this 5-dimensional contact manifold. In particular, we focus on loops arising as families of the unit conormal bundles of knots in R3, and I will explain a topological method to compute the monodromy on the Legendrian contact homology in degree 0 induced by those loops. As an application, we get examples of non-contractible loops of Legendrian tori which are contractible in the space of smoothly embedded tori. This is joint work with Marián Poppr.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/04/21
16:00-17:00 Online
Pre-registration required. See our seminar webpage.
Masaki Taniguchi (Kyoto University)
Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilization (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Masaki Taniguchi (Kyoto University)
Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilization (JAPANESE)
[ Abstract ]
Wall's stabilization principle suggests that exotic phenomena in dimension four in the orientable category disappear after taking connected sums with sufficiently many S2xS2. Since most known exotic pairs of closed 4-manifolds become diffeomorphic after one stabilization, a natural question was: is a single S2xS2 enough? Recently, Jianfeng Lin constructed an exotic diffeomorphism on a closed 4-manifold-a diffeomorphism topologically isotopic to the identity but not smoothly isotopic-that survives one stabilization. In this talk, we provide a relative exotic diffeomorphism on a compact contractible 4-manifold that survives two stabilizations. This gives the first exotic phenomenon in the orientable category that survives two stabilizations. This is joint work with Sungkyung Kang and Junghwan Park.
[ Reference URL ]Wall's stabilization principle suggests that exotic phenomena in dimension four in the orientable category disappear after taking connected sums with sufficiently many S2xS2. Since most known exotic pairs of closed 4-manifolds become diffeomorphic after one stabilization, a natural question was: is a single S2xS2 enough? Recently, Jianfeng Lin constructed an exotic diffeomorphism on a closed 4-manifold-a diffeomorphism topologically isotopic to the identity but not smoothly isotopic-that survives one stabilization. In this talk, we provide a relative exotic diffeomorphism on a compact contractible 4-manifold that survives two stabilizations. This gives the first exotic phenomenon in the orientable category that survives two stabilizations. This is joint work with Sungkyung Kang and Junghwan Park.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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
2026/05/12
16:00-17:00 Online
Pre-registration required. See our seminar webpage.
Sanghoon Kwak (Seoul National University)
Mapping class group of Infinite graph: 'Big' Out(Fn) (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Sanghoon Kwak (Seoul National University)
Mapping class group of Infinite graph: 'Big' Out(Fn) (ENGLISH)
[ Abstract ]
Algom-Kfir and Bestvina introduced the mapping class groups of locally finite, infinite graphs in 2021. Since Out(Fn) can be realized as the mapping group of a finite graph, their construction may be viewed as a "big" version of Out(Fn). In this talk, we survey the algebraic and coarse geometric properties of these groups and discuss a relationship with mapping class groups of infinite-type surfaces ("big mapping class groups"). This talk is based on joint work with Ryan Dickmann, George Domat, and Hannah Hoganson, in various collaborations.
[ Reference URL ]Algom-Kfir and Bestvina introduced the mapping class groups of locally finite, infinite graphs in 2021. Since Out(Fn) can be realized as the mapping group of a finite graph, their construction may be viewed as a "big" version of Out(Fn). In this talk, we survey the algebraic and coarse geometric properties of these groups and discuss a relationship with mapping class groups of infinite-type surfaces ("big mapping class groups"). This talk is based on joint work with Ryan Dickmann, George Domat, and Hannah Hoganson, in various collaborations.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
