Tuesday Seminar on Topology

Seminar information archive ~03/27Next seminarFuture seminars 03/28~

Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2019/01/15

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Yusuke Kuno (Tsuda University)
Generalized Dehn twists on surfaces and homology cylinders (JAPANESE)
[ Abstract ]
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.