Topology from a prospect of group invariant orderings and its applications
| Project/Area Number |
15K17540
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Kyoto University (2015, 2018)
Osaka University (2016-2017) |
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Principal Investigator |
Tetsuya Ito 京都大学, 理学研究科, 准教授 (00710790)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 三次元多様体 / 接触幾何 / 組みひも群 / オープンブック分解 / 順序群 / 一般化ねじれ元 / 接触構造 / 強擬正組みひも / 擬正組みひも / 写像類群 |
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| Outline of Final Research Achievements |
I studied various problems related to low-dimensional topology inspired by invariant group orderings. In joint works with Keiko Kawamuro (Univ. Iowa) we established a theory of open book foliation and constructed a mthod to study contact 3-manifolds by topological method. In particular, we studied the relation between Fractional Dehn twist coefficients (FDTC), a quantity closely related to orderings of braid groups or mapping class groups, and topology or contact structures. We also studied isolated orderings, and a condition to exist (not to exist) geeralized torsion elements or bi-ordering on 3-manifold groups.
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| Academic Significance and Societal Importance of the Research Achievements |
低次元トポロジーの研究は様々な違う分野からの刺激やアイディアを受けて発展を続けている分野であるが、順序構造との関連は近年になり着目されるようになった視点である。群の順序という代数的な構造が幾何的な情報と関連していること、またいくつかのトポロジーの問題を解くことに有用であることがわかり、低次元トポロジーの研究の新しい手法の一つを開拓できた。
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Report
(5 results)
Research Products
(26 results)
