Research of spatial graph invariants based on algebraic topology
Project/Area Number |
21740046
|
Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
Geometry
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Research Institution | Tokyo Woman's Christian University |
Principal Investigator |
NIKKUNI Ryo 東京女子大学, 現代教養学部, 准教授 (00401878)
|
Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | 低次元トポロジー / 空間グラフ / 結び目 / 絡み目 / 不変量 / ΔY変換 / Conway-Gordonの定理 / 直線型空間グラフ / 基本群 / 初等イデアル / △Y変換 / 結び目内在 / 絡み目内在 / 局所変形 / Vassiliev不変量 |
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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Report
(4 results)
Research Products
(39 results)