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Seminar on Geometric Complex Analysis
Seminar information archive ～04/17｜Next seminar｜Future seminars 04/18～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2017/10/30
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Masahide Kato (Sophia University)
Odd dimensional complex analytic Kleinian groups
Masahide Kato (Sophia University)
Odd dimensional complex analytic Kleinian groups
[ Abstract ]
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 $\mathrm{PGL}(2n+2,\mathbf{C})$ which act on $\mathbf{P}^{2n+1}$, 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 $\mathbf{P}^{n}$ in $\mathbf{P}^{2n+1}$ 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 $\mathrm{PGL}(2n+2,\mathbf{C})$ which act on $\mathbf{P}^{2n+1}$, 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 $\mathbf{P}^{n}$ in $\mathbf{P}^{2n+1}$ 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.
