2019 Fiscal Year Final Research Report
Orderings in 3-manifold groups
| Project/Area Number |
16K05149
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | 不変順序 / ３次元多様体 / 共役ねじれ元 / 正規生成元 / 正規閉包 |
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| Outline of Final Research Achievements |
We proposed a conjecture which claims that a 3-manifold group is not bi-orderable if and only if it admits a generalized torsion element. Although this is still open, we solved it for various families of 3-manifolds such as Seifert fibered manifolds. As a byproduct, we found a way to construct generalized torsion elements for Fibonacci groups and their generalizations. Also, we studied the normal closures of slope elements in knot groups and their inclusion relation.
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| Free Research Field |
トポロジー
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| Academic Significance and Societal Importance of the Research Achievements |
低次元トポロジーにおいて，最も注目されているのは3次元多様体といっても過言ではない．本研究では，3次元多様体の基本群に注目し，群論的な問題に対してトポロジーの成果を用いて取り組んだ．へガード・フロア理論からの要請もあって，基本群が許容する不変順序の研究は喫緊の課題であり，引き続き国内外における研究継続が望まれる．
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