bounded cohomology and symplectic topology around mapping class groups

围绕映射类群的有界上同调和辛拓扑

• 批准号: 20540056
• 负责人: KANDA Yutaka
• 金额: $ 2.41万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540056/
• 关键词: 位相幾何学; レフシェッツ束; 写像類群; 有界コホモロジー; K理論; 写像数群

To investigate bounded cohomology of mapping class groups of compact surfaces and to show the boundedness of Morita-Mumford classes, I studied a certain class of finite dimensional representations of these groups, with special focus on estimating their range. Also I tried to apply Takefumi Nosaka' work, that on the interrelationship between quandle cohomology and Lefshetz fibrations over the sphere, to estimate the Gromov semi-norm of the 1^<st> Morita-Mumford classes.

为了研究紧致曲面映射类群的有界上同调并显示 Morita-Mumford 类的有界性，我研究了这些群的某一类有限维表示，特别关注估计它们的范围。我还尝试应用 Takefum​​i Nosaka 的工作，即有关 qudle 上同调和球面上 Lefshetz 纤维之间相互关系的工作，来估计 1^<st> Morita-Mumford 类的 Gromov 半范数。