Tuesday Seminar on Topology
Seminar information archive ~10/09|Next seminar|Future seminars 10/10~
Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
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Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2009/07/14
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
作間 誠 (広島大学)
The Cannon-Thurston maps and the canonical decompositions
of punctured-torus bundles over the circle.
作間 誠 (広島大学)
The Cannon-Thurston maps and the canonical decompositions
of punctured-torus bundles over the circle.
[ Abstract ]
To each once-punctured-torus bundle over the circle
with pseudo-Anosov monodromy, there are associated two tessellations of the complex plane:
one is the triangulation of a horosphere induced by the canonical decomposition into ideal
tetrahedra, and the other is a fractal tessellation
given by the Cannon-Thurston map of the fiber group.
In this talk, I will explain the relation between these two tessellations
(joint work with Warren Dicks).
I will also explain the relation of the fractal tessellation and
the "circle chains" of double cusp groups converging to the fiber group
(joint work with Caroline Series).
If time permits, I would like to discuss possible generalization of these results
to higher-genus punctured surface bundles.
To each once-punctured-torus bundle over the circle
with pseudo-Anosov monodromy, there are associated two tessellations of the complex plane:
one is the triangulation of a horosphere induced by the canonical decomposition into ideal
tetrahedra, and the other is a fractal tessellation
given by the Cannon-Thurston map of the fiber group.
In this talk, I will explain the relation between these two tessellations
(joint work with Warren Dicks).
I will also explain the relation of the fractal tessellation and
the "circle chains" of double cusp groups converging to the fiber group
(joint work with Caroline Series).
If time permits, I would like to discuss possible generalization of these results
to higher-genus punctured surface bundles.