Integrality of Homfly (1,1)tangle invariants
Abstract
Given an invariant J(K) of a knot K, the corresponding (1,1)tangle invariant J'(K)=J(K)/J(U) is defined as the quotient of J(K) by its value J(U) on the unknot U. We prove here that J' is always an integer 2variable Laurent polynomial when J is the Homfly satellite invariant determined by decorating K with any eigenvector of the meridian map in the Homfly skein of the annulus. Specialisation of the 2variable polynomials for suitable choices of eigenvector shows that the (1,1)tangle irreducible quantum sl(N) invariants of K are integer 1variable Laurent polynomials.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606336
 Bibcode:
 2006math......6336M
 Keywords:

 Mathematics  Geometric Topology;
 57M25
 EPrint:
 10 pages, including several interspersed figures