Study on structures of knot space and knot invariants

• 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
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 結び目理論 / 結び目不変量 / 局所変形 / 結び目空間

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 Issue: 07 Pages: 1250068-1250068
  • 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
  • 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 Issue: 04 Pages: 125005511-9
  • DOI: 10.1142/s0218216511010097
  • Peer Reviewed
• [Journal Article] Differences of Alexander polynomials for knots caused by a single crossing change (2012)
  • Author(s): Yasutaka NAKANISHI and Yuki OKADA
  • Journal Title: Topology and its Applications Volume: Vol.159 Issue: 4 Pages: 1016-1025
  • 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
• [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(東京都)(招待講演)
• [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
• [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(沖縄県)(招待講演)
• [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
• [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
• [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
• [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
• [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
• [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.)(招待講演)
• [Presentation] The differences of Alexander polynomials cased by a single crossing change (2010)
  • Author(s): Y.Nakanishi, Y.Okada
  • Organizer: International Conference Japan-Mexico on Topology and Its Applications
  • Place of Presentation: University of Colima, Colima, (Mexico)(招待講演)
• [Presentation] Notes on sharp moves 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, (山形県)(招待講演)
• [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: The Sixth Asian School of Knots and Related Topics
  • Place of Presentation: Nankai University(中国)
• [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: 日本数学会年会トポロジー分科会
  • Place of Presentation: 慶應義塾大学矢上キャンパス(神奈川県)
• [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
• [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(山形県)
• [Remarks]
  • URL: http://www.math.kobe-u.ac.jp/home-j/index7-1-10.html
• [Remarks]
  • URL: http://www.math.kobe-u.ac.jp/home-j/index7-1-10.html