bounded cohomology and symplectic topology around mapping class groups

• Project/Area Number: 20540056
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido University
• Principal Investigator: KANDA Yutaka 北海道大学, 大学院・理学研究院, 助教 (30280861)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 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

Research Abstract

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.