Lower bounds for the number of positive and negative crossings in oriented link diagrams. (English) Zbl 1420.57025
Summary: We obtain a simple lower bound for the number of positive (resp. negative) crossings in oriented link diagrams in terms of the maximal (resp. minimal) degree of the Jones polynomial.
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
Software:
KnotInfoReferences:
| [1] | J. C. Cha and C. Livingston, KnotInfo: Table of Knot Invariants, http://www.indiana. edu/ knotinfo. |
| [2] | V. F. R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985), no. 1, 103-111. · Zbl 0564.57006 |
| [3] | L. H. Kauffman, State models and the Jones polynomial, Topology 26 (1987), no. 3, 395-407. · Zbl 0622.57004 |
| [4] | K. Murasugi, On invariants of graphs with applications to knot theory, Trans. Amer. Math. Soc. 314 (1989), no. 1, 1-49. · Zbl 0726.05051 |
| [5] | A. Stoimenow, On some restrictions to the values of the Jones polynomial, Indiana Univ. Math. J. 54 (2005), no. 2, 557-574. · Zbl 1076.57015 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
