2011 Fiscal Year Final Research Report
Handlebody-knots and topology
| Project/Area Number |
21740035
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | University of Tsukuba |
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Principal Investigator |
ISHII Atsushi 筑波大学, 数理物質系, 助教 (00531451)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 位相幾何学 / 結び目理論 |
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| Research Abstract |
A handlebody-knot is a handlebody embedded in the 3-sphere. Two handlebody-knots are equivalent if one can be transformed into the other by an isotopy of the 3-sphere. A handlebody-knot is a natural generalization of a knot, and is closely related to a spatial graph and a 3-manifold. The results of this study are as follows : I defined a normalized Yamada polynomial. I provided methods to detect the irreducibility of a handlebody-knot by using quandle coloring invariants. I introduced the IH-complex on the set of spatial trivalent graphs, and evaluated the IH-distance by using invariants.
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Research Products
(18 results)
