New development of the theory of infinite dimensional Teichmuller spaces: construction of moduli spaces

无限维Teichmuller空间理论的新进展：模空间的构造

• 批准号: 23740102
• 负责人: FUJIKAWA Ege
• 金额: $ 2.83万
• 依托单位: Chiba University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740102/
• 关键词: 複素解析学; リーマン面; 擬等角写像; タイヒミュラー空間; 写像類群; モジュライ空間; 双曲幾何学; 擬等角写像類群; タイヒミュラーモジュラー群; タイヒミュラー空間論

On the classification of the Teichmuller modular transformations in infinite dimensional Teichmuller spaces, we investigated properties of transformations of infinite discrete type and those of divergent type. We also observed asymptotic Teichmuller modular transformations acting on asymptotic Teichmuller spaces and obtained a sufficient condition to be of finite order. Furthermore, for a subgroup of the quasiconformal mapping class group that is stationary, we observed discontinuity of the action on the space of asymptotically conformal classes.

关于无限维Teichmuller空间中Teichmuller模变换的分类，研究了无限离散型和发散型变换的性质。我们还观察了作用于渐近Teichmuller空间的渐近Teichmuller模变换，并得到了渐近Teichmuller模变换是有限阶的充分条件。进一步，对于拟共形映射类群的平稳子群，我们观察到作用在渐近共形类空间上的不连续。

项目成果

Coherence of limit points in the fiber over the asymptotic Teichmuller space

渐近 Teichmuller 空间上光纤极限点的相干性

• 作者: Takeshi Miura;Go Hirasawa;Sin-Ei Takahasi and Takahiro Hayata;Ikehata M. & Itou H;Takeshi Miura and Go Hirasawa,;Ege Fujikawa;Ege Fujikawa
• 通讯作者: Ege Fujikawa

Discontinuity of asymptotic Teichmuller modular group

渐近 Teichmuller 模群的不连续性

• 发表时间: 2012
• 期刊: Contemporary Mathematics
• 作者: O.Hatori;Y.Iida;S.Stevic;S.Ueki;野津裕史;梅原守道;H. Notsu;A.K. Sharma and S. Ueki;羽鳥理;Ege Fujikawa;Ege Fujikawa;Ege Fujikawa;Michiyuki Watanabe;野津裕史，田端正久;渡邊 道之;Morimichi Umehara;H. Notsu;梅原守道;S. Ueki;Morimichi Umehara;Ege Fujikawa
• 通讯作者: Ege Fujikawa

Peripheral quasiconformal automorphism groups and the Nielsen realization problem

外围拟共形自同构群和 Nielsen 实现问题

• 作者: Seto Michio;Suda Sho;Taniguchi Tetsuji;Ege Fujikawa
• 通讯作者: Ege Fujikawa

Topological characterization of the asymptotically trivial mapping class group

渐进平凡映射类群的拓扑表征

• 发表时间: 2014
• 期刊: Handbook of Group Actions (Higher Education Press and International Press)
• 作者: O.Hatori;Y.Iida;S.Stevic;S.Ueki;野津裕史;梅原守道;H. Notsu;A.K. Sharma and S. Ueki;羽鳥理;Ege Fujikawa
• 通讯作者: Ege Fujikawa

Coherence of limit points in the fibers over the asymptotic Teichmuller space

渐进 Teichmuller 空间上纤维极限点的相干性

• 发表时间: 2014
• 期刊: Computational Methods and Function Theory
• 影响因子: 2.1
• 作者: O.Hatori;Y.Iida;S.Stevic;S.Ueki;野津裕史;梅原守道;H. Notsu;A.K. Sharma and S. Ueki;羽鳥理;Ege Fujikawa;Ege Fujikawa
• 通讯作者: Ege Fujikawa