The mapping class groups of Heegaard splittings
Project/Area Number |
26800028
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Geometry
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Research Institution | Hiroshima University |
Principal Investigator |
Koda Yuya 広島大学, 理学研究科, 准教授 (20525167)
|
Research Collaborator |
ISHIKAWA Masaharu
OZAWA Makoto
CHO Sangbum
SEO Arim
|
Project Period (FY) |
2014-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
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Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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Keywords | 3 次元多様体 / Heegaard 分解 / 写像類群 / 結び目 / トンネル / ヘンペル距離 / 国際情報交換 韓国 / 円盤複体 |
Outline of Final Research Achievements |
Every closed orientable 3-manifold can be decomposed into 2 handlebodies by cutting it along a closed orientable surface of genus g. This decomposition is called a Heegaard splitting. Given a Heegaard splitting, the group of isotopy classes of orientation-preserving self-homeomorphisms of the 3-manifold that preserve the splitting is called the Goeitz group of the splitting. The aim of this project was to provide a finite presentation of the Goeritz group for every reducible genus-2 Heegaard splitting, and it has completed successfully. As applications or related topics, we obtained the following: (1) a sufficient condition that the Goeritz group of a higher genus Heegaard splitting admits a finite generationg set; (2) the "uniqueness" of (1,1)-decompositions of 2-bridge knots; (3) a characterization of "knotted" subspaces in terms of "relative" homotopy type of knots in the subspaces.
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Report
(4 results)
Research Products
(32 results)