Embeddings of manifold-graphs

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400097
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Komazawa University
• Principal Investigator: Ozawa Makoto 駒澤大学, 総合教育研究部, 教授 (50308160)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: ３次元球面 / 多重分岐曲面 / 埋め込み / 部分多様体 / 橋分解

Outline of Final Research Achievements

(1) For 3-submanifolds of the 3-sphere, we studied and obtained results on ①trivialization of knots in it by a homotopy, ②relation between the existence of Seifert surfaces and Dehn surgery along links, ③realization of Fox's re-embeddings by twistings.
(2) From embeddings of multibranched surfaces into 3-manifolds, we defined the genus of it, and showed that the genus is bounded by the sum of the number of branches and sectors above.
(3) We constructed knots with destabilized bridge spheres of arbitrary high bridge number.

Free Research Field

結び目理論