Knots and Polynomials
Received:June 01, 2008  Revised:October 06, 2008
Key Word: knot   Jones polynomial   Laurent polynomial.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10771023) and the Liaoning Educational Committee (Grant No.2009A418).
Author NameAffiliation
You Fa HAN School of Mathematics, Liaoning Normal University, Liaoning 116029, P. R. China 
Xiao Sha MA School of Mathematics, Liaoning Normal University, Liaoning 116029, P. R. China 
Hits: 2409
Download times: 1404
Abstract:
      In this paper, we deal with some corresponding relations between knots and polynomials by using the basic properties of knot polynomials (such as, some special values of knot polynomials, the Arf invariant and derivative of knot polynomials). We give necessary and sufficient conditions that a Laurent polynomial with integer coefficients, whose breadth is less than five, is the Jones polynomial of a certain knot.
Citation:
DOI:10.3770/j.issn:1000-341X.2010.02.008
View Full Text  View/Add Comment  Download reader