| Project/Area Number |
16K17591
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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 | Tsuda University (2018)
Aichi University of Education (2016-2017) |
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Principal Investigator |
Inoue Ayumu 津田塾大学, 学芸学部, 准教授 (10610149)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 対称性 / カンドル / 結び目 / ファイバー結び目 / 曲面結び目 / 正多胞体 / 領域交差交換 / トポロジー |
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| Outline of Final Research Achievements |
A quandle is an algebra which has high compatibility with symmetry. Symmetries with which a knot is equipped are important properties to understanding the knot. The aim of this research is utilizing quandle theory to investigate several symmetries of knots. In accordance with this program, the researcher mainly obtained the following results: (1) Several quandles describing rotational symmetries of regular cells are isomorphic to knot quandles of some concrete knots. (2) The structure of a fibered knot, as a fiber bundle, is completely reflected in its knot quandle. (3) (joint work with Ryo Shimizu) We introduced a local move of a knot diagram, named a region freeze crossing change, and showed that this move is related to a region crossing change along with mirror symmetry.
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| Academic Significance and Societal Importance of the Research Achievements |
紐状の物質の絡まりは，例えば高分子や DNA など，自然界に多く存在する．その絡まりが備える「対称性」を理解することは，物性や現象を理解する上においても，非常に重要である．本研究を通じて結び目が備える対称性に対する理解が進んだことは，結び目理論の発展のみならず，科学全般の進展においても意義がある．
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