Embeddings of manifold-graphs
| Project/Area Number |
26400097
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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 | Komazawa University |
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Principal Investigator |
Ozawa Makoto 駒澤大学, 総合教育研究部, 教授 (50308160)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | ３次元球面 / 多重分岐曲面 / 埋め込み / 部分多様体 / 橋分解 / ホモロジー群 / トーション / 種数 / ３次元多様体 / ヒーガード分解 / マイナー / 障害集合 / knot homotopy / transient / persistent / bridge sphere / destabilized / multibranched surface / embedding / obstruction |
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| Outline of Final Research Achievements |
(1) For 3-submanifolds of the 3-sphere, we studied and obtained results on ①trivialization of knots in it by a homotopy, ②relation between the existence of Seifert surfaces and Dehn surgery along links, ③realization of Fox's re-embeddings by twistings.
(2) From embeddings of multibranched surfaces into 3-manifolds, we defined the genus of it, and showed that the genus is bounded by the sum of the number of branches and sectors above.
(3) We constructed knots with destabilized bridge spheres of arbitrary high bridge number.
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Report
(4 results)
Research Products
(33 results)
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[Presentation] Embeddings of multibranched surfaces2015
Author(s)
Makoto Ozawa
Organizer
The Spatial Graphs Special Session at the AMS Sectional Meeting
Place of Presentation
California State University, Fullerton
Year and Date
2015-10-24
Related Report
Int'l Joint Research / Invited
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