Studies on band surgery and Dehn surgery on links

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K03483
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 11020:Geometry-related
• Research Institution: Kindai University
• Principal Investigator: Jong In Dae 近畿大学, 理工学部, 准教授 (30587788)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: デーン手術 / 矯飾的デーン手術 / 例外的デーン手術 / 結び目 / 絡み目 / 局所変形操作

Outline of Final Research Achievements

1) We prove that any non-trivial two-bridge knot admit no purely cosmetic surgery pairs. The paper containing the result had published in a refereed journal as a collaboration paper with Kazuhiro Ichihara, Toshio Saito, and Thomas Mattman. 2) We calculate several invariants to show alternating knots and Montesinos knots admit no purely cosmetic surgeries. We obtain a partial result for this study. 3) We give a complete list of hyperbolic two-bridge links which can admit complete exceptional surgeries. The paper containing the result had submitted to a refereed journal as a collaboration paper with Kazuhiro Ichihara and Hidetoshi Masai.

Free Research Field

結び目理論，低次元トポロジー

Academic Significance and Societal Importance of the Research Achievements

本研究で得られた成果のうち，学術雑誌に掲載された論文「Two-bridge knots admit no purely cosmetic surgeries」は，今後のデーン手術研究，特に矯飾的デーン手術研究における重要なマイルストーンとなります．さまざまな不変量の計算を駆使して全ての2橋結び目に対して未解決問題が解決できたことは，結果自体が重要であることに加え，研究手法として1つの道筋を構成したことに意義があります．