2006 Fiscal Year Final Research Report Summary
Geometric group theory and hyperbolic geometry
| Project/Area Number |
17540057
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tohoku University |
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Principal Investigator |
FUJIWARA Koji Tohoku University, Graduate School of Science, Associate Professor, 大学院理学研究科, 助教授 (60229078)
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| Co-Investigator(Kenkyū-buntansha) |
SHIOYA Takashi Tohoku University, Graduate School of Science, Professor, 大学院理学研究科, 教授 (90235507)
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| Project Period (FY) |
2005 – 2006
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| Keywords | JSJ decomposition / 3-manifolds / Graph decomposition |
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| Research Abstract |
In a joint work with Papasoglu, Fujiwara established a theory of "JSJ-decomposition" for finitely presented group along slender subgroups. The result is a far reach generalization of the theorem by Rips-Sela on the JSJ-decomposition along cyclic subgroups.
A group is said "slender" if all of its subgroups are finitely generated. For example, any finitely generated abelian groups and nilpotent groups are slender, while a free group of rank at least two is not slender. The work is published in 2006.
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