%0 Journal Article %T Integrality of Homfly (1,1)-tangle invariants %A H. R. Morton %J Mathematics %D 2006 %I arXiv %R 10.2140/agt.2007.7.327 %X 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 2-variable 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 2-variable polynomials for suitable choices of eigenvector shows that the (1,1)-tangle irreducible quantum sl(N) invariants of K are integer 1-variable Laurent polynomials. %U http://arxiv.org/abs/math/0606336v1