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複素解析幾何セミナー
過去の記録 ～06/27｜次回の予定｜今後の予定 06/28～
| 開催情報 | 月曜日 10:30～12:00 数理科学研究科棟(駒場) 128号室 |
|---|---|
| 担当者 | 平地 健吾, 高山 茂晴 |
2017年10月30日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
加藤 昌英 氏 (上智大学)
Odd dimensional complex analytic Kleinian groups
加藤 昌英 氏 (上智大学)
Odd dimensional complex analytic Kleinian groups
[ 講演概要 ]
In this talk, I would explain an idea to construct a higher dimensional analogue of the classical Kleinian group theory. For a group G of a certain class of discrete subgroups of PGL(2n+2,C) which act on P2n+1, there is a canonical way to define the region of discontinuity, on which G acts properly discontinuously. General principle in the discussion is to regard Pn in P2n+1 as a single point. We can consider the quotient space of the discontinuity region by the action of G. Though the Ahlfors finiteness theorem is hopeless because of a counter example, the Klein combination theorem and the handle attachment can be defined similarly. Any compact quotients which appear here are non-Kaehler. In the case n=1, we explain a new example of compact quotients which is related to a classical Kleinian group.
In this talk, I would explain an idea to construct a higher dimensional analogue of the classical Kleinian group theory. For a group G of a certain class of discrete subgroups of PGL(2n+2,C) which act on P2n+1, there is a canonical way to define the region of discontinuity, on which G acts properly discontinuously. General principle in the discussion is to regard Pn in P2n+1 as a single point. We can consider the quotient space of the discontinuity region by the action of G. Though the Ahlfors finiteness theorem is hopeless because of a counter example, the Klein combination theorem and the handle attachment can be defined similarly. Any compact quotients which appear here are non-Kaehler. In the case n=1, we explain a new example of compact quotients which is related to a classical Kleinian group.
