## トポロジー火曜セミナー

開催情報 火曜日　17:00～18:30　数理科学研究科棟(駒場) 056号室 河野 俊丈, 河澄 響矢, 北山 貴裕, 逆井卓也 http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html Tea: 16:30 - 17:00 コモンルーム

### 2019年01月15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

Generalized Dehn twists on surfaces and homology cylinders (JAPANESE)
[ 講演概要 ]
This is a joint work with Gwénaël Massuyeau (University of Burgundy). Lickorish's trick describes Dehn twists along simple closed curves on an oriented surface in terms of surgery of 3-manifolds. We discuss one possible generalization of this description to the situation where the curve under consideration may have self-intersections. Our result generalizes previously known computations related to the Johnson homomorphisms for the mapping class groups and for homology cylinders. In particular, we obtain an alternative and direct proof of the surjectivity of the Johnson homomorphisms for homology cylinders, which was proved by Garoufalidis-Levine and Habegger.