| Project/Area Number |
26400099
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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 | Nihon University |
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Principal Investigator |
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| Research Collaborator |
ICHIHARA kazuhiro
TERAGAITO masakazu
MIYAZAKI katura
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 幾何学 / トポロジー / ３次元多様体 / 結び目 / デーン手術 / ザイフェルト多様体 / L-空間 / 共役ねじれ元 / Dehn手術 / L-空間結び目 / twisting operation / 結び目種数 / ４次元結び目種数 / characterizing slope / スロープ予想 / 結び目のバンド和 / 基本群の両側不変順序 / generalized torsion / Seifert空間 / twisting / seiferter / L-空間手術 |
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| Outline of Final Research Achievements |
We study Seifert surgeries on knots, which are exceptional Dehn surgeries, from a networking viewpoint. In particular, a joint work with Baker (University of Miami) extends a foundation of Seifert Surgery Network by generalizing a notion of seiferter. Using seiferters which have key roles in a study of Seifert Surgery Network, we study a relationship between L-space knots and twisting operation and provide a plenty of twist families of knots which contain infinitely many L-space knots. Furthermore, recently in a joint work with Baker we gave a necessary condition for a twist family of knots to contain infinitely many L-space knots.
We also study generalized torsion elements in 3-manifold groups, and a joint work with Teragaito (Hiroshima University) proves that the fundamental group of a geometric 3-manifold which is not hyperbolic has no bi-ordering if and only if it has a generalized torsion element.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究ではザイフェルト手術のネットワークの視点からの研究で導入されたSeifert Surgery Networkの連結性に関連してseiferterの概念を一般化し、研究の枠組みを拡張した。また、ネットワークの視点を現在活発に研究されているL-空間結び目の研究に応用し、豊富な例の構成をはじめ、L-空間結び目への幾何的制限を与えることに成功した。証明の過程でタイトな接触構造をサポートするファイバー結び目に関する興味深い事実を明らかにした。最近注目されている３次元多様体の基本群の共役ねじれ元についても基本群の両側不変順序と関連した研究を進展させ、今後の研究の新たな方向を与えることができた。
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