本文印刷
全画面プリント
トポロジー火曜セミナー
過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
| 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 |
2007年07月03日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
金 英子 氏 (東京工業大学情報理工学研究科)
Two invariants of pseudo--Anosov mapping classes: hyperbolic volume vs dilatation
(joint work with Mitsuhiko Takasawa)
Tea: 16:00 - 16:30 コモンルーム
金 英子 氏 (東京工業大学情報理工学研究科)
Two invariants of pseudo--Anosov mapping classes: hyperbolic volume vs dilatation
(joint work with Mitsuhiko Takasawa)
[ 講演概要 ]
We concern two invariants of pseudo-Anosov mapping classes.
One is the dilatation of pseudo--Anosov maps and the other is the volume
of mapping tori. To study how two invariants are related, fixing a surface
we represent a mapping class by using the standard generator set and compute
these two for all pseudo--Anosov mapping classes with up to some word length.
In the talk, we observe two properties:
(1) The ratio of the topological entropy (i.e. logarithm of the dilatation) to
the volume is bounded from below by some positive constant which only
depends on the surface.
(2) The conjugacy class having the minimal dilatation reaches the minimal volume.
On the observation (1), in case of the mapping class group of a once--punctured
torus, we give a concrete lower bound of the ratio.
We concern two invariants of pseudo-Anosov mapping classes.
One is the dilatation of pseudo--Anosov maps and the other is the volume
of mapping tori. To study how two invariants are related, fixing a surface
we represent a mapping class by using the standard generator set and compute
these two for all pseudo--Anosov mapping classes with up to some word length.
In the talk, we observe two properties:
(1) The ratio of the topological entropy (i.e. logarithm of the dilatation) to
the volume is bounded from below by some positive constant which only
depends on the surface.
(2) The conjugacy class having the minimal dilatation reaches the minimal volume.
On the observation (1), in case of the mapping class group of a once--punctured
torus, we give a concrete lower bound of the ratio.
