Generalization of quandles and their applications
| Project/Area Number |
23654027
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Osaka City University (2013)
Hiroshima University (2011-2012) |
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Principal Investigator |
KAMADA SEIICHI 大阪市立大学, 大学院理学研究科, 教授 (60254380)
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| Co-Investigator(Renkei-kenkyūsha) |
SAEKI Osamu 九州大学, マス・フォア・インダストリ研究所, 教授 (30201510)
OHTSUKI Tomotada 京都大学, 数理解析研究所, 教授 (50223871)
KAMADA Naoko 名古屋市立大学, システム自然科学研究科, 教授 (60419687)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | トポロジー / カンドル / 結び目 / バイカンドル / 対称カンドル / 高次元結び目 / 仮想結び目 |
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| Research Abstract |
As generalizations of a quandle, we studied biquandles and symmetric quandles. The notion of a biquandle was re-defined by a system of axioms, and two additional structures, called T-structure and V-structure, were introduced. These structures are related to virtual knots and twisted virtual knots. We also gave a method of constructing a biquandle from a given quandle. By the method, one can easily and effectively construct many biquandles. Presentation of a symmetric quandle was studied, and a method of obtaining a presentation of the fundamental symmetric quandle of a manifold knot was introduced.
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Report
(4 results)
Research Products
(36 results)
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[Presentation] Charts for 3-dimensional braids2013
Author(s)
Seiichi Kamada
Organizer
アメリカ数学会, 特別セッション「Algebraic Structures in Knot Theory III」
Place of Presentation
University of California at Riverside, カリフォルニア, 米国
Year and Date
2013-11-03
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[Presentation] Charts for 3-dimensional braids
Author(s)
S. Kamada
Organizer
Western Fall Sectional Meeting, American Mathematical Society
Place of Presentation
University of California at Riverside, California, 米国
Related Report
Invited
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