Seifert fiber spaces, L-spaces, left-orderability of fundamental groups and Dehn surgery
| 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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Report
(6 results)
Research Products
(45 results)
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[Presentation] Non-characterizing slopes for knots2016
Author(s)
Kimihiko Motegi
Organizer
2016 International Conference on Low-Dimensional Topology
Place of Presentation
Southwest Jiaotong University, Sichuan, China
Year and Date
2016-06-14
Related Report
Int'l Joint Research / Invited
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[Presentation] L-space knots and twisting operation2014
Author(s)
Kimihiko Motegi
Organizer
A Satellite Conference of Seoul ICM 2014, Knots and Low Dimensional Manifolds
Place of Presentation
BEXCO Convention & Exhibition Center II, Busan, Korea
Year and Date
2014-08-25
Related Report
Invited
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[Book] 幾何学序論2018
Author(s)
市原一裕, 鈴木正彦, 茂手木公彦
Total Pages
227
Publisher
日本評論社
ISBN
9784535788596
Related Report
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