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Tuesday Seminar on Topology
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2020/07/14
17:30-18:30 Online
Joint with Lie Groups and Representation Theory Seminar. Pre-registration required. See our seminar webpage.
Takayuki Okuda (Hiroshima University)
Kobayashi's properness criterion and totally geodesic submanifolds in locally symmetric spaces (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with Lie Groups and Representation Theory Seminar. Pre-registration required. See our seminar webpage.
Takayuki Okuda (Hiroshima University)
Kobayashi's properness criterion and totally geodesic submanifolds in locally symmetric spaces (JAPANESE)
[ Abstract ]
Let G be a Lie group and X a homogeneous G-space. A discrete subgroup of G acting on X properly is called a discontinuous group for X. We are interested in constructions and classifications of discontinuous groups for a given X.
It is well-known that if the isotropies of G on X are compact, any closed subgroup acts on X properly. However, the cases where the isotropies are non-compact, the same claim does not hold in general.
Let us consider the case where G is a linear reductive. In this situation, T. Kobayashi [Math. Ann. (1989)], [J. Lie Theory (1996)]
gave a criterion for the properness of the action on a homogeneous G-space X of closed subgroups in G.
In this talk, we consider homogeneous G-spaces of reductive types realized as families of totally geodesic submanifolds in non-compact Riemannian symmetric spaces. As a main result, we give a translation of Kobayashi's criterion within the framework of Riemannian geometry. In particular, for a torsion-free discrete subgroup of G, the criterion can be stated in terms of totally geodesic submanifolds in the Riemannian locally symmetric space corresponding to the subgroup in G.
[ Reference URL ]Let G be a Lie group and X a homogeneous G-space. A discrete subgroup of G acting on X properly is called a discontinuous group for X. We are interested in constructions and classifications of discontinuous groups for a given X.
It is well-known that if the isotropies of G on X are compact, any closed subgroup acts on X properly. However, the cases where the isotropies are non-compact, the same claim does not hold in general.
Let us consider the case where G is a linear reductive. In this situation, T. Kobayashi [Math. Ann. (1989)], [J. Lie Theory (1996)]
gave a criterion for the properness of the action on a homogeneous G-space X of closed subgroups in G.
In this talk, we consider homogeneous G-spaces of reductive types realized as families of totally geodesic submanifolds in non-compact Riemannian symmetric spaces. As a main result, we give a translation of Kobayashi's criterion within the framework of Riemannian geometry. In particular, for a torsion-free discrete subgroup of G, the criterion can be stated in terms of totally geodesic submanifolds in the Riemannian locally symmetric space corresponding to the subgroup in G.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
