2011 Fiscal Year Final Research Report
Research of spatial graph invariants based on algebraic topology
| Project/Area Number |
21740046
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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 | Tokyo Woman's Christian University |
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Principal Investigator |
NIKKUNI Ryo 東京女子大学, 現代教養学部, 准教授 (00401878)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 低次元トポロジー / 空間グラフ / 結び目 / 絡み目 / 不変量 |
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| Research Abstract |
(1) We obtained the result about Alexander invariants of spatial graphs, in particular, the elementary ideals of Alexander matrix with respect to a homomorphism from the fundamental group of the spatial graph complement to the infinite cyclic group.(2) We gave several classification theorems for spatial theta curves and spatial complete graph on four vertices by the finite type invariants.(3) We obtained the result about the intrinsic knottedness and linkedness for graphs, in particular, an integer-version of the Conway-Gordon type theorem and a new kind of intrinsic nontriviality for graphs.
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