## Lie群論・表現論セミナー

開催情報 火曜日　16:30～18:00　数理科学研究科棟(駒場) 126号室 小林俊行 https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2012年11月20日(火)

16:30-17:30   数理科学研究科棟(駒場) 126号室
Ali Baklouti 氏 (Sfax University)
On the geometry of discontinuous subgroups acting on some homogeneous spaces (ENGLISH)
[ 講演概要 ]
Let $G$ be a Lie group, $H$ a closed subgroup of $G$ and \\Gamma$a discontinuous subgroup for the homogeneous space$G/H$. I first introduce the deformation space${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$of the action of$\\Gamma$on$G/H$in the sense of Kobayashi and some of its refined versions, namely the Clifford--Klein space of deformations of the form${\\mathcal{X}}=\\Gamma \\backslash G/H$. The deformation space${\\mathcal{T}}^{G_o}(\\Gamma, G,H)$of marked$(G,H)$-structures on${\\mathcal{X}}$in the sense of Goldman is also introduced. As an important motivation, I will explain the connection between the spaces${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$and${\\mathcal{T}}^{G_o}(\\Gamma, G, H)\$ and study some of their topological features, namely the rigidity in the sense of Selberg--Weil--Kobayashi and the stability in the sense of Kobayashi--Nasrin. The latter appears to be of major interest to write down the connection explicitly.