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Tuesday Seminar on Topology
Seminar information archive ～04/30｜Next seminar｜Future seminars 05/01～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | HABIRO Kazuo, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2018/11/27
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Motoko Kato (The University of Tokyo)
Fixed points for group actions on non-positively curved spaces (JAPANESE)
Motoko Kato (The University of Tokyo)
Fixed points for group actions on non-positively curved spaces (JAPANESE)
[ Abstract ]
In this talk, we introduce a fixed point property of groups which is a broad generalization of Serre's property FA, and give a criterion for groups to have such a property. We also apply the criterion to show that various generalizations of Thompson's group T have fixed points whenever they act on finite dimensional non-positively curved metric spaces, including CAT(0) spaces. Since Thompson's group T is known to have fixed point free actions on infinite dimensional CAT(0) spaces, it follows that there is a group which acts on infinite dimensional CAT(0) spaces without global fixed points, but not on finite dimensional ones.
In this talk, we introduce a fixed point property of groups which is a broad generalization of Serre's property FA, and give a criterion for groups to have such a property. We also apply the criterion to show that various generalizations of Thompson's group T have fixed points whenever they act on finite dimensional non-positively curved metric spaces, including CAT(0) spaces. Since Thompson's group T is known to have fixed point free actions on infinite dimensional CAT(0) spaces, it follows that there is a group which acts on infinite dimensional CAT(0) spaces without global fixed points, but not on finite dimensional ones.
