Convergence group actions and their depth

• Project/Area Number: 25800036
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Aoyama Gakuin University (2014-2016); Kyoto University (2013)
• Principal Investigator: MATSUDA Yoshifumi 青山学院大学, 理工学部, 助教 (60549294)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 収束群作用 / 相対的双曲群 / 不変生成 / トンプソン群 / 双曲群

Outline of Final Research Achievements

We studied convergence group actions by introducing their depth, which measures their closeness to geometrically finite convergence group actions. Based on result obtained by other researchers in research period, it turned out that there exists a group which has a convergence group action of infinite depth.
We also studied invariable generation of groups. A group which has a nonelementary convergence group action is not invariably generated. We showed that certain groups of piecewise linear homeomorphisms of the real line, such as Thompson group F, are invariably generated.