Research of the topology on spatial graphs and algebraic invariants

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540094
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• 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): 2012-04-01 – 2015-03-31
• Keywords: 低次元トポロジー / 空間グラフ / 結び目 / 絡み目 / ハンドル体 / 不変量

Outline of Final Research Achievements

We studied spatial graph theory, that is a research of graphs embedded in 3-space from a viewpoint of low dimensional topology. More concretely, we have the following results: (1) We gave a homotopy classification theorem for two-component spatial graphs up to neighborhood equivalence by the elementary divisor-type invariant. (2) We gave an application of reduced Wu invariants of spatial graphs to the research of the intrinsic symmetry for graphs. (3) We studied twisted Alexander invariants of spatial graphs and obtained some results about classification problem for spatial graphs. (4) We obtained the results about the intrinsic knottedness for the Heawood graph.

Free Research Field

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