On the Rasmussen (Beliakova-Wehrli) invariant for links

• Project/Area Number: 23840021
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: ABE Tetsuya 京都大学, 数理解析研究所, 研究員(GCOE) (00614009)
• Project Period (FY): 2011 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 結び目 / 絡み目 / ラスムッセン不変量 / Beliakova-Wehrli 不変量 / コバノフホモロジー / リーホモロジー / コンコーダンス群 / スライス結び目 / リボン結び目 / スライス・リボン予想 / ハンドル図式(カービー図式) / ４次元多様体 / カービー計算 / 低次元トポロジー / バンド手術

Research Abstract

We studied the Beliakova-Wehrli invariant for a link which is a generalization of the Rasmussen invariant for a knot. We also studied a slice knot which is closely related to the Rasmussen invariant.

Research Products

• [Journal Article] Unoriented band-surgery on knots and links (2013)
  • Author(s): T.Abe, T. Kanenobu
  • Journal Title: to appear in Kobe Journal of Mathematics
  • Peer Reviewed
• [Journal Article] Annulus twist and diffeomorphic 4-manifolds (2013)
  • Author(s): T.Abe, I. Jong, Y. Omae and M. Takeuchi
  • Journal Title: Math. Proc. Cambridge Philos. Soc Pages: 1-17
  • URL: http://arxiv.org/pdf/1209.0361v2.pdf
  • Peer Reviewed
• [Journal Article] Omae's knot and 12a990 are ribbon (2012)
  • Author(s): T.Abe and M. Tange
  • Journal Title: RIMS Kokyuroku Volume: 1812 Pages: 34-42
  • URL: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1812-04.pdf
• [Journal Article] The unknotting number and band-unknotting number of a knot (2012)
  • Author(s): T.Abe, R. Hanaki and R. Higa
  • Journal Title: Osaka J. Math Volume: 49 Pages: 523-550
  • NAID: 120005986505
  • URL: http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.ojm/1340197938
  • Peer Reviewed
• [Journal Article] State cycles which represent the canonical class of Lee's homology of a knot (2012)
  • Author(s): T.Abe
  • Journal Title: Topology and its Applications Volume: Volume 159 Issue: 4 Pages: 1146-1158
  • DOI: 10.1016/j.topol.2011.11.042
  • Peer Reviewed
• [Journal Article] Omae's knot and 12a990 are ribbon (2012)
  • Author(s): T. Abe and M. Tange
  • Journal Title: RIMS Kokyuroku Volume: 1812
• [Journal Article] The unknotting number and band-unknotting number of a knot (2012)
  • Author(s): Tetsuya Abe, Ryo Hanaki, Ryuji Higa
  • Journal Title: Osaka J.Math. Volume: (印刷中)
  • NAID: 120005986505
  • Peer Reviewed
• [Journal Article] The Rasmussen invariant of a homogeneous knot (2011)
  • Author(s): T.Abe
  • Journal Title: Proc. Amer. Math. Soc Volume: 139 Pages: 2647-2656
  • URL: http://arxiv.org/pdf/1003.5392v1.pdf
  • Peer Reviewed
• [Journal Article] The Rasmussen invariant of a homogeneous knot (2011)
  • Author(s): Tetsuya Abe
  • Journal Title: Proc.Amer.Math.Soc. Volume: 139 Pages: 2647-2656
  • Peer Reviewed
• [Presentation] Omae's knot and 12a990 are ribbon (2012)
  • Author(s): 安部哲哉
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
  • Year and Date: 2012-09-20
• [Presentation] Annulus twists and diffeomorphic 4-manifolds (2012)
  • Author(s): Tetsuya Abe
  • Organizer: The 6th European Congress of Mathematics, Jagellionian University
  • Place of Presentation: Poland
  • Year and Date: 2012-07-05
• [Presentation] Unoriented band surgery on knots and link (2012)
  • Author(s): 安部哲哉
  • Organizer: 日本数学会春季総合分科会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-26
• [Presentation] Unoriented band surgery on knots and links (2012)
  • Author(s): Tetsuya Abe
  • Organizer: 日本数学会
  • Place of Presentation: Tokyo(日本)
  • Year and Date: 2012-03-26
• [Presentation] Omae's knot and 12_a990 are ribbon (2012)
  • Author(s): 安部哲哉
  • Organizer: 日本数学会 秋季総合分科会
  • Place of Presentation: 九州大学
• [Remarks]
  • URL: http://yumemusou.web.fc2.com