Actions of infinite simple groups
| Project/Area Number |
24654011
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TSUBOI Takashi 東京大学, 数理(科)学研究科(研究院), 教授 (40114566)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 幾何学 / 代数学 / トポロジー / 微分同相群 / 幾何学的群論 / 無限単純群 |
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| Outline of Final Research Achievements |
There are many infinite simple groups which have natural actions on spaces. Consider the set X of the unions of the conjugate classes of a nontrivial element and its inverse in an infinite simple group G. For 2 such unions, one union is always contained in a power of the other. This phenominon gives rise to a metric on X. We studied properties of this metric on X by using the action of G on some space. For a nontrivial subset K which is closed under taking inverses, any element of G can be written as a product of conjugates of elements of K. The minimal number of conjugates defines a norm on the group G. We clarified the relationship between the metric on X and the norm and quasimorphisms on G. We also showed that in certain homeomorphism groups, every elemet can be written as one commutator.
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Report
(4 results)
Research Products
(5 results)
