2017 Fiscal Year Final Research Report
PN-equivalence of diagrams of singular surface-knots and its application
Project/Area Number |
16H07125
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Research Category |
Grant-in-Aid for Research Activity Start-up
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Allocation Type | Single-year Grants |
Research Field |
Geometry
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Research Institution | Osaka City University |
Principal Investigator |
Kawamura Kengo 大阪市立大学, 大学院理学研究科, 数学研究所専任研究所員 (00780727)
|
Project Period (FY) |
2016-08-26 – 2018-03-31
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Keywords | 特異曲面結び目 / はめ込み曲面結び目 / ダイアグラム / 3重点数 / カンドル / カンドルコサイクル不変量 |
Outline of Final Research Achievements |
We study about diagrams of singular surface-knots. An invariant of a surface-knot, called the quandle cocycle invariant, is obtained from quandle homology groups. Although this invariant usually does not become an invariant of a singular surface-knot, we can modify quandle homology groups to yield an invariant of a singular surface-knot by focusing on a local move of its diagram. It is known that the triple point number of a surface-knot is not equal to one and that the triple point number of a sphere-knot is not equal to two or three. In this research, we prove that the triple point number of an orientable singular surface-knot (with arbitrary number of nodes) is not equal to one and that the triple point number of a singular sphere-knot with one node is not equal to two or three.
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Free Research Field |
数物系科学
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