Text only print
Full screen print
Tuesday Seminar on Topology
Seminar information archive ～04/24｜Next seminar｜Future seminars 04/25～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2007/07/03
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
金 英子 (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)
金 英子 (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)
[ Abstract ]
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.
