2016 Fiscal Year Final Research Report
Convergence group actions and their depth
| Project/Area Number |
25800036
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Aoyama Gakuin University (2014-2016)
Kyoto University (2013) |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 収束群作用 / 相対的双曲群 / 不変生成 / トンプソン群 |
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| 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.
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| Free Research Field |
数物系科学
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