Study on structures of knot space and knot invariants

2011 Fiscal Year Final Research Report

• Project/Area Number: 21540081
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Kobe University
• Principal Investigator: NAKANISHI Yasutaka 神戸大学, 大学院・理学研究科, 教授 (70183514)
• Co-Investigator(Kenkyū-buntansha): SATOH Shin 神戸大学, 大学院・理学研究科, 准教授 (90345009)
• Co-Investigator(Renkei-kenkyūsha): OHYAMA Yoshiyuki 東京女子大学, 現代教養学部, 教授 (80223981) ; UCHIDA Yoshiaki 神戸薬科大学, 薬学部, 教授 (80280890)
• Project Period (FY): 2009 – 2011
• Keywords: 結び目理論 / 結び目不変量 / 局所変形

Research Abstract

We have studied structures and invariants of knots by local moves to research the structure of knot space. We give a result on the structure of knot space with respect to crossing changes and Alexander polynomials. We give a method to construct infinite families of composite knots with# unknotting number one.

Research Products

• [Journal Article] Twin groups of virtual 2-bridge knots and almost classical knots (2012)
  • Author(s): T. Nakamura, Y. Nakanishi, S. Satoh, and Y. Tomiyama
  • Journal Title: Journal of Knot Theory and Its Ramifications Volume: 21-8 Pages: 1250095-1-18
  • DOI: DOI:10.1142/S021821651250068X
  • Peer Reviewed
• [Journal Article] Notes on sharp moves (2012)
  • Author(s): T. Nakamura and Y. Nakanishi
  • Journal Title: Journal of Knot Theory and Its Ramifications Volume: 21-7 Pages: 1250068-1-20
  • Peer Reviewed
• [Journal Article] On non-self local moves (2012)
  • Author(s): Y. Nakanishi, T. Shibuya, T. Tsukamoto, and A. Yasuhara
  • Journal Title: Journal of Knot Theory and Its Ramifications Volume: 21-4 Pages: 1250055-1-9
  • DOI: DOI:10.1142/S0218216511010097
  • Peer Reviewed
• [Journal Article] The differences of Alexander polynomials caused by a single crossing change (2012)
  • Author(s): Y. Nakanishi and Y. Okada
  • Journal Title: Topology and Its Applications Volume: 159-4 Pages: 1016-1025
  • DOI: DOI:10.1016/j.topol.2011,11,023
  • Peer Reviewed
• [Presentation] On knot diagrams (2012)
  • Author(s): 中西康剛
  • Organizer: 研究集会「結び目の展望」
  • Place of Presentation: 早稲田大学教育学部
  • Year and Date: 20120317-18
• [Presentation] 結び目の局所変形について (2011)
  • Author(s): 中西康剛
  • Organizer: 2011琉球結び目セミナー
  • Place of Presentation: 那覇市伝統工芸館会議室
  • Year and Date: 20110906-07
• [Presentation] Notes on sharpmoves for knots (2010)
  • Author(s): 中村拓司, 中西康剛
  • Organizer: 東北結び目セミナー
  • Place of Presentation: 遊学館,山形
  • Year and Date: 20101022-24
• [Presentation] The differences of Alexander polynomials caused by a single crossing change (2010)
  • Author(s): Y. Nakanishi and Y. Okada
  • Organizer: International Conference Japan-Mexico on Topology and Its Applications
  • Place of Presentation: University of Colima, Colima, Mexico
  • Year and Date: 20100927-1001
• [Presentation] Local moves and Gordian complexes, IV (2010)
  • Author(s): Y. Nakanishi
  • Organizer: The 2nd TAPU-KOOK Joint Seminar on Knots and Related Topics
  • Place of Presentation: Kyungpook National University, Daegu, Korea
  • Year and Date: 20100726-30
• [Presentation] Alexander polynomials of knots which are transformed into the trefoil knot by a single crossing change (2010)
  • Author(s): 中西康剛
  • Organizer: 日本数学会トポロジー分科会
  • Place of Presentation: 慶応義塾大学矢上キャンパス
  • Year and Date: 20100324-27
• [Presentation] Alexander polynomials of knots which are transformed into the trefoil knot by a single crossing change (2010)
  • Author(s): Y. Nakanishi
  • Organizer: The Sixth Asian School of Knots and Related Topics
  • Place of Presentation: Nankai University, P. R. China
  • Year and Date: 20100125-28
• [Presentation] Alexander polynomials of knots which are transformed into the trefoil knot by a single crossing change (2009)
  • Author(s): 中西康剛
  • Organizer: 東北結び目セミナー
  • Place of Presentation: 山形テルサ,山形
  • Year and Date: 20091017-19
• [Remarks]
  • URL: http://www.math.kobe-u.ac.jp/home-j/index7-1-10.html