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Tuesday Seminar on Topology
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2024/01/16
17:00-18:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Jin Miyazawa (The University of Tokyo)
A gauge theoretic invariant of embedded surfaces in 4-manifolds and exotic P2-knots (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Jin Miyazawa (The University of Tokyo)
A gauge theoretic invariant of embedded surfaces in 4-manifolds and exotic P2-knots (JAPANESE)
[ Abstract ]
When two embeddings of surfaces on a 4-dimensional manifold are given, if they are topologically isotopic but not smoothly isotopic, we call them a pair of exotic surfaces. While there is a great deal of study of exotic surfaces in 4-manifolds, studies of closed exotic surfaces in S4 are limited. In particular, the existence of orientable exotic surfaces in S4 remains unknown to date. There are some examples of non-orientable exotic surfaces in S4, including the initial example given by Finashin-Kreck-Viro in 1988, but all such cases have genus greater than or equal to 5. The difficulty in detecting exotic surfaces in S4 is to prove that two embeddings of surfaces are not smoothly isotopic. All examples of exotic non-orientable surfaces in S4 have been detected by proving the 4-manifolds obtained by the double branched covers are exotic. If we attempt to apply this technique to low-genus non-orientable surfaces in S4, we have to discover exotic small 4-manifolds, which is known to be difficult. In this seminar, we construct an invariant for embedded surfaces in 4-manifolds using Real Seiberg-Witten theory. As an application, we give an infinite family of exotic embeddings into S4 for the real projective plane.
[ Reference URL ]When two embeddings of surfaces on a 4-dimensional manifold are given, if they are topologically isotopic but not smoothly isotopic, we call them a pair of exotic surfaces. While there is a great deal of study of exotic surfaces in 4-manifolds, studies of closed exotic surfaces in S4 are limited. In particular, the existence of orientable exotic surfaces in S4 remains unknown to date. There are some examples of non-orientable exotic surfaces in S4, including the initial example given by Finashin-Kreck-Viro in 1988, but all such cases have genus greater than or equal to 5. The difficulty in detecting exotic surfaces in S4 is to prove that two embeddings of surfaces are not smoothly isotopic. All examples of exotic non-orientable surfaces in S4 have been detected by proving the 4-manifolds obtained by the double branched covers are exotic. If we attempt to apply this technique to low-genus non-orientable surfaces in S4, we have to discover exotic small 4-manifolds, which is known to be difficult. In this seminar, we construct an invariant for embedded surfaces in 4-manifolds using Real Seiberg-Witten theory. As an application, we give an infinite family of exotic embeddings into S4 for the real projective plane.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
