Study of groups of measure-preserving homeomorphisms and volume-preserving diffeomorphisms of noncompact manifolds

非紧流形的保测同胚群和保体积微分同胚群的研究

• 批准号: 22540081
• 负责人: YAGASAKI Tatsuhiko
• 金额: $ 1.33万
• 依托单位: Kyoto Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540081/
• 关键词: 幾何学; トポロジー; 微分同相群; 無限次元多様体; 同相群; 一様同相写像; 一様位相; Whitney位相

We studied topological properties of groups of diffeomorphisms and homeomorphisms of any on-compact manifold M. Under the compact-open C∞topology, we extended a parametrized version of Moser’s theorem for volume forms to the non-compact case. As for the Whitney C∞ topology, we howed That the pair of the group of diffeomorphisms of M and the subgroup of those with compact support is Locally homeomorphic to the pair of countable box product and small box product of l2.As for the uniform topology, we also obtained some deformation theorems for spaces of uniform embeddings and Groups of uniform homeomorphisms.

我们研究了任何紧致流形 M 的微分同胚和同胚群的拓扑性质。在紧开 C∞ 拓扑下，我们将体积形式的 Moser 定理的参数化版本扩展到非紧情况。对于Whitney C∞拓扑，我们得到M的微分同胚群和紧支持子群的对与l2的可数盒积和小盒积对局部同胚。对于均匀拓扑，我们还得到了均匀嵌入空间和均匀同胚群的一些变形定理。

项目成果

Uniform and compact-open topologies on homeomorphism groups of noncompact manifolds

非紧流形同胚群上的均匀紧开拓扑

• 发表时间: 2012
• 作者: 矢ヶ崎達彦;Whitney
• 通讯作者: Whitney

Groups of volume-preserv ?ing diffeomorphisms of noncompact mani ?folds and mass flow toward ends, Satellite Thematic Session ? Geometric Topology

非紧流形的保体积微分同胚组和流向末端的质量流，卫星专题会议？

• 发表时间: 2012
• 作者: 矢ヶ崎達彦;Whitney;R. Goto;矢ヶ崎達彦;矢ヶ崎達彦;R. Goto;矢ヶ崎達彦;R. Goto;後藤竜司;後藤竜司;T.Yagasaki
• 通讯作者: T.Yagasaki

Topological (Π ∞.l2, Σ ∞ l2) ?factors of diffeomorphism groups of noncompact manifolds

非紧流形微分同胚群的拓扑 (Π ∞.l2, Σ ∞ l2) 因子

• 发表时间: 2010
• 作者: 矢ヶ崎達彦;Whitney;R. Goto;矢ヶ崎達彦;矢ヶ崎達彦;R. Goto;矢ヶ崎達彦;R. Goto;後藤竜司;後藤竜司;T.Yagasaki;R. Goto;矢ヶ崎達彦;Ryushi Goto;矢ヶ崎達彦;R. Goto and K. Hayano;T.Yagasaki;R. Goto;矢ヶ崎達彦;後藤竜司;矢ヶ崎達彦;矢ヶ崎達彦;後藤竜司;Ryushi Goto;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;T.Yagasaki;Tatsuhiko Yagasaki;矢ヶ崎達彦;矢ヶ崎達彦;矢ク崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦
• 通讯作者: 矢ヶ崎達彦

Groups of uniform homeomorphisms of covering spaces

覆盖空间的一致同胚群

• 发表时间: 2012
• 作者: 越野 克久;酒井 克郎;秦泉寺雅夫;矢ヶ崎 達彦;秦泉寺雅夫;嶺 幸太郎;矢ヶ崎 達彦;矢ヶ崎 達彦
• 通讯作者: 矢ヶ崎 達彦

Diffeomorphism groups of non-compact manifolds with the compact ?open C∞topology

具有紧?开C∞拓扑的非紧流形的微分同胚群

• 发表时间: 2010
• 作者: 矢ヶ崎達彦;Whitney;R. Goto;矢ヶ崎達彦;矢ヶ崎達彦;R. Goto;矢ヶ崎達彦;R. Goto;後藤竜司;後藤竜司;T.Yagasaki;R. Goto;矢ヶ崎達彦;Ryushi Goto;矢ヶ崎達彦;R. Goto and K. Hayano;T.Yagasaki;R. Goto;矢ヶ崎達彦;後藤竜司;矢ヶ崎達彦;矢ヶ崎達彦;後藤竜司;Ryushi Goto;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;T.Yagasaki;Tatsuhiko Yagasaki;矢ヶ崎達彦;矢ヶ崎達彦;矢ク崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;矢ヶ崎達彦;T.Yagasaki
• 通讯作者: T.Yagasaki