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Tuesday Seminar on Topology
Seminar information archive ～06/21｜Next seminar｜Future seminars 06/22～
| 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 |
2024/04/23
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.
Tatsumasa Suzuki (Meiji University)
Pochette surgery on 4-manifolds and the Ozsváth--Szabó d-invariants of Brieskorn homology 3-spheres (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tatsumasa Suzuki (Meiji University)
Pochette surgery on 4-manifolds and the Ozsváth--Szabó d-invariants of Brieskorn homology 3-spheres (JAPANESE)
[ Abstract ]
This talk consists of the following two research contents:
I. The boundary sum of S1×D3 and D2×S2 is called a pochette. The pochette surgery, which is a generalization of Gluck surgery and a special case of torus surgery, was discovered by Zjuñici Iwase and Yukio Matsumoto in 2004. For a pochette P embedded in a 4-manifold X, a pochette surgery on X is the operation of removing the interior of P and gluing P by a diffeomorphism of the boundary of P. In this talk, we focus on the fact that pochette surgery is a surgery with a cord and the 2-sphere S2, and attempt to classify the diffeomorphism type of pochette surgery on the 4-sphere S4.
II. In 2003, Peter Ozsváth and Zoltán Szabó introduced a homology cobordism invariant for homology 3-spheres called a d-invariant. In this talk, we present new computable examples by refining the Karakurt--Şavk formula for any Brieskorn homology 3-sphere Σ(p,q,r) with p is odd and pq+pr−qr=1. Furthermore, by refining the Can--Karakurt formula for the d-invariant of any Σ(p,q,r), we also introduce the relationship with the d-invariant of Σ(p,q,r) and those of lens spaces.
This talk includes contents of joint work with Motoo Tange (University of Tsukuba).
[ Reference URL ]This talk consists of the following two research contents:
I. The boundary sum of S1×D3 and D2×S2 is called a pochette. The pochette surgery, which is a generalization of Gluck surgery and a special case of torus surgery, was discovered by Zjuñici Iwase and Yukio Matsumoto in 2004. For a pochette P embedded in a 4-manifold X, a pochette surgery on X is the operation of removing the interior of P and gluing P by a diffeomorphism of the boundary of P. In this talk, we focus on the fact that pochette surgery is a surgery with a cord and the 2-sphere S2, and attempt to classify the diffeomorphism type of pochette surgery on the 4-sphere S4.
II. In 2003, Peter Ozsváth and Zoltán Szabó introduced a homology cobordism invariant for homology 3-spheres called a d-invariant. In this talk, we present new computable examples by refining the Karakurt--Şavk formula for any Brieskorn homology 3-sphere Σ(p,q,r) with p is odd and pq+pr−qr=1. Furthermore, by refining the Can--Karakurt formula for the d-invariant of any Σ(p,q,r), we also introduce the relationship with the d-invariant of Σ(p,q,r) and those of lens spaces.
This talk includes contents of joint work with Motoo Tange (University of Tsukuba).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
