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トポロジー火曜セミナー
過去の記録 ～04/20｜次回の予定｜今後の予定 04/21～
| 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 |
| セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2018年04月17日(火)
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Tamás Kálmán 氏 (東京工業大学)
Tight contact structures on Seifert surface complements and knot invariants (ENGLISH)
Tea: Common Room 16:30-17:00
Tamás Kálmán 氏 (東京工業大学)
Tight contact structures on Seifert surface complements and knot invariants (ENGLISH)
[ 講演概要 ]
In joint work with Daniel Mathews, we examined complements of standard Seifert surfaces of special alternating links and used Honda's method to enumerate those tight contact structures on them whose dividing sets are isotopic to the link. The number turns out to be the leading coefficient of the Alexander polynomial. The proof is rather combinatorial in nature; for example, the Euler classes of the contact structures are identified with `hypertrees' in a certain hypergraph. Using earlier results with Hitoshi Murakami and Alexander Postnikov, this yields a connection between contact topology and the Homfly polynomial. We also found that the contact invariants of our structures form a basis for the sutured Floer homology of the manifold.
In joint work with Daniel Mathews, we examined complements of standard Seifert surfaces of special alternating links and used Honda's method to enumerate those tight contact structures on them whose dividing sets are isotopic to the link. The number turns out to be the leading coefficient of the Alexander polynomial. The proof is rather combinatorial in nature; for example, the Euler classes of the contact structures are identified with `hypertrees' in a certain hypergraph. Using earlier results with Hitoshi Murakami and Alexander Postnikov, this yields a connection between contact topology and the Homfly polynomial. We also found that the contact invariants of our structures form a basis for the sutured Floer homology of the manifold.
