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トポロジー火曜セミナー
過去の記録 ～06/27｜次回の予定｜今後の予定 06/28～
| 開催情報 | 火曜日 17:00～18:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也, 葉廣和夫 |
| セミナーURL | https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2011年01月25日(火)
16:30-17:30 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
春田 力 氏 (東京大学大学院数理科学研究科)
シート数が小さい曲面結び目の自明化について (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
春田 力 氏 (東京大学大学院数理科学研究科)
シート数が小さい曲面結び目の自明化について (JAPANESE)
[ 講演概要 ]
A connected surface smoothly embedded in mathbbR4 is called a surface-knot. In particular, if a surface-knot F is homeomorphic to the 2-sphere or the torus, then it is called an S2-knot or a T2-knot, respectively. The sheet number of a surface-knot is an invariant analogous to the crossing number of a 1-knot. M. Saito and S. Satoh proved some results concerning the sheet number of an S2-knot. In particular, it is known that an S2-knot is trivial if and only if its sheet number is 1, and there is no S2-knot whose sheet number is 2. In this talk, we show that there is no S2-knot whose sheet number is 3, and a T2-knot is trivial if and only if its sheet number is 1.
A connected surface smoothly embedded in mathbbR4 is called a surface-knot. In particular, if a surface-knot F is homeomorphic to the 2-sphere or the torus, then it is called an S2-knot or a T2-knot, respectively. The sheet number of a surface-knot is an invariant analogous to the crossing number of a 1-knot. M. Saito and S. Satoh proved some results concerning the sheet number of an S2-knot. In particular, it is known that an S2-knot is trivial if and only if its sheet number is 1, and there is no S2-knot whose sheet number is 2. In this talk, we show that there is no S2-knot whose sheet number is 3, and a T2-knot is trivial if and only if its sheet number is 1.
