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Tuesday Seminar on Topology
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
Next seminar
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 $S^1 \times D^3$ and $D^2 \times S^2$ 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 $S^2$, and attempt to classify the diffeomorphism type of pochette surgery on the 4-sphere $S^4$.
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 $\Sigma(p,q,r)$ with $p$ is odd and $pq+pr-qr=1$. Furthermore, by refining the Can--Karakurt formula for the $d$-invariant of any $\Sigma(p,q,r)$, we also introduce the relationship with the $d$-invariant of $\Sigma(p,q,r)$ 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 $S^1 \times D^3$ and $D^2 \times S^2$ 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 $S^2$, and attempt to classify the diffeomorphism type of pochette surgery on the 4-sphere $S^4$.
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 $\Sigma(p,q,r)$ with $p$ is odd and $pq+pr-qr=1$. Furthermore, by refining the Can--Karakurt formula for the $d$-invariant of any $\Sigma(p,q,r)$, we also introduce the relationship with the $d$-invariant of $\Sigma(p,q,r)$ 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
