polynomial invariants of knots and related theory

2008 Fiscal Year Final Research Report

• Project/Area Number: 19740035
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Osaka City University (2008); Kyoto University (2007)
• Principal Investigator: STOIMENOW Alexander Osaka City University (60444452)
• Project Period (FY): 2007 – 2008
• Keywords: braid group / archiral knot / Hecke algebra / link polynomial

Research Abstract

15以上の各奇数交点数でのachiralな結び目の構成を完成した.
「行列-不・量-対数は'曲体"で直'的に近'される」という予想を-\'きにδ証明した.BurauとLawrence-Krammer現の稠密性,非自明なJones
多項式の問題と幾何的な性質を持つ閉じた3次組み紐についても研究を行った.

Research Products

• [Journal Article] Bennequin's inequality and the positivity of the signature (2008)
  • Author(s): Stoimenow A
  • Journal Title: Trans. Amer. Math. Soc 360(10) Pages: 5173-5199
  • Peer Reviewed
• [Journal Article] Tait's conjectures and odd crossing number amphicheiral knots (2008)
  • Author(s): Stoimenow A
  • Journal Title: Bull. Amer. Math. Soc. (N.S.) 45(2) Pages: 285-291
  • Peer Reviewed
• [Journal Article] Generating functions, Fibonacci numbers and rational knots, J. (2007)
  • Author(s): Stoimenow A
  • Journal Title: Algebra 310(2) Pages: 491-525
  • Peer Reviewed
• [Journal Article] Square numbers and polynomial invariants of archiral knots (2007)
  • Author(s): Stoimenow A,
  • Journal Title: Math. Z. 255(4) Pages: 703-719
  • Peer Reviewed
• [Journal Article] On cabled knots and Vassiliev invariants (not) contained in knot polynomials (2007)
  • Author(s): Stoimenow A,
  • Journal Title: Canad. J. Math., 59(2) Pages: 418-448
  • Peer Reviewed
• [Journal Article] Graphs, determinants of knots and hyperbolic volume (2007)
  • Author(s): Stoimenow A,
  • Journal Title: Pacific J. Math 232(2) Pages: 423-451
  • Peer Reviewed
• [Presentation] Lie groups Burau representation, and non-conjugate braids with the same closure link (2009)
  • Author(s): Stoimenow A
  • Organizer: The Fifth East Asia School of Knots and Related Topics
  • Place of Presentation: 慶州,韓国
  • Year and Date: 20090112-16
• [Presentation] Lie groups, Burau representation, and non-conjugate braids with the same closure link (2008)
  • Author(s): Stoimenow A
  • Organizer: The First Topology Workshop KAIST
  • Place of Presentation: 韓国
  • Year and Date: 20080812-14
• [Remarks]
  • URL: http://mathsci.kaist.ac.kr/~stoimeno/