2012 Fiscal Year Final Research Report
Hurwitz action on systems of braids
| Project/Area Number |
23840026
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Gunma National College of Technology (2012)
Hiroshima University (2011) |
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Principal Investigator |
YAGUCHI Yoshiro 群馬工業高等専門学校, 一般教科(自然科学), 講師 (90613018)
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| Project Period (FY) |
2011 – 2012
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| Keywords | ブレイド群 / Hurwitz作用 / ブレイド状曲面 / コード |
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| Research Abstract |
1) Hurwitz equivalence on systems of braids is studied, which can be used in the study of braided surfaces. We obtained some invariants of the Hurwitz equivalence on the systems of braids by using the first Johnson homomorphism of the braid group. Then, we found some invariants of braided surfaces.2) A cord is a simple curve on a punctured disk, which connects two punctures. We introduced diagrams which represent isotopy classes of cords. Using such diagrams, we made up a list of all isotopy classes of cords on a 3-times punctured disk. As a result, it was shown that they are completely parameterized by 3 non-negative integers.
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