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Tuesday Seminar on Topology
Seminar information archive ～05/02｜Next seminar｜Future seminars 05/03～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2020/12/15
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Eiko Kin (Osaka University)
Braids, triangles and Lissajous curve (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Eiko Kin (Osaka University)
Braids, triangles and Lissajous curve (JAPANESE)
[ Abstract ]
The purpose of this talk is to introduce Lissajous 3-braids. Suppose we have a closed curve on the plane, and we consider the periodic motion of n points along the closed curve. If the motion is collision-free, then we get a braid obtained from the trajectory of the set of n points in question. In this talk, we consider 3-braids coming from the periodic motion of 3 points on Lissajous curves. We classify Lissajous 3-braids and present a parametrization in terms of natural numbers together with slopes. We also discuss some properties of pseudo-Anosov stretch factors for Lissajous 3-braids. The main tool is the shape sphere --- the configuration space of the oriented similarity classes of triangles. This is a joint work with Hiroaki Nakamura and Hiroyuki Ogawa.
[ Reference URL ]The purpose of this talk is to introduce Lissajous 3-braids. Suppose we have a closed curve on the plane, and we consider the periodic motion of n points along the closed curve. If the motion is collision-free, then we get a braid obtained from the trajectory of the set of n points in question. In this talk, we consider 3-braids coming from the periodic motion of 3 points on Lissajous curves. We classify Lissajous 3-braids and present a parametrization in terms of natural numbers together with slopes. We also discuss some properties of pseudo-Anosov stretch factors for Lissajous 3-braids. The main tool is the shape sphere --- the configuration space of the oriented similarity classes of triangles. This is a joint work with Hiroaki Nakamura and Hiroyuki Ogawa.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
