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Tuesday Seminar on Topology
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2013/01/22
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Jarek Kedra (University of Aberdeen)
On the autonomous metric of the area preserving diffeomorphism
of the two dimensional disc. (ENGLISH)
Jarek Kedra (University of Aberdeen)
On the autonomous metric of the area preserving diffeomorphism
of the two dimensional disc. (ENGLISH)
[ Abstract ]
Let D be the open unit disc in the Euclidean plane and let
G:=Diff(D, area) be the group of smooth compactly supported
area-preserving diffeomorphisms of D. A diffeomorphism is called
autonomous if it is the time one map of the flow of a time independent
vector field. Every diffeomorphism in G is a composition of a number
of autonomous diffeomorphisms. The least amount of such
diffeomorphisms defines a norm on G. In the talk I will investigate
geometric properties of such a norm.
In particular I will construct a bi-Lipschitz embedding of the free
abelian group of arbitrary rank to G. I will also show that the space
of homogeneous quasi-morphisms vanishing on all autonomous
diffeomorphisms in G is infinite dimensional.
This is a joint work with Michael Brandenbursky.
Let D be the open unit disc in the Euclidean plane and let
G:=Diff(D, area) be the group of smooth compactly supported
area-preserving diffeomorphisms of D. A diffeomorphism is called
autonomous if it is the time one map of the flow of a time independent
vector field. Every diffeomorphism in G is a composition of a number
of autonomous diffeomorphisms. The least amount of such
diffeomorphisms defines a norm on G. In the talk I will investigate
geometric properties of such a norm.
In particular I will construct a bi-Lipschitz embedding of the free
abelian group of arbitrary rank to G. I will also show that the space
of homogeneous quasi-morphisms vanishing on all autonomous
diffeomorphisms in G is infinite dimensional.
This is a joint work with Michael Brandenbursky.
