| Budget Amount *help |
¥4,100,000 (Direct Cost: ¥4,100,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2002: ¥1,700,000 (Direct Cost: ¥1,700,000)
|
|---|
| Research Abstract |
The goal of this project is to study several problems on infinite discrete groups from the view point of geometry.
"Geometric group theory" has its root in the pionear work by Gromov, and has been developed mainly in USA and Europe in the last 15 years or so.
It is a dynamic field where one can apply classical combinatorial group theory, hyperbolic geometry, low dimensional topology, and the theory of mapping class groups. Unfortunately, there has not been much activities of this field in Japan yet.
During the three years, we not only conducted our research, but also tried to put a foundation of the research activities of this field in Japan.
One of our research themes has been on isometric actions of group on CAT(0) spaces. The notion of "CAT(0) spaces" was introduced by Gromov to geodesic metric spaces as a generalization of complete, simply-connected Riemannian manifolds, called "Hadamard manifolds".
Given a discrete group G, it is important and useful to find a metric space X on which G acts on by isometries, properly. One classical example is the action of a lattice subgroup in a Lie group on its symmetric space.
It would be interesting to find such X of minimal dimensions. In this direction, there has been a work by Brady-Crisp. We developed their work and found an answer to their question, found new examples, and formulated further questions in the paper "Parabolic isometries of CAT(0) spaces and CAT(0) dimensions", Fujiwara, Koji ; Shioya, Takashi ; Yamagata, Saeko. Algebr.Geom.Topol.4(2004), 861-892
|
