Integrality of Homfly 1-tangle invariants

Morton, Hugh R ORCID: 0000-0002-8524-2695 (2007) Integrality of Homfly 1-tangle invariants. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 7 (1). pp. 327-338.

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Official URL: http://dx.doi.org/10.2140/agt.2007.7.327

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 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.

Item Type:	Article
Additional Information:	10 pages, including several interspersed figures
Uncontrolled Keywords:	math.GT, math.GT, 57M25
Depositing User:	Symplectic Admin
Date Deposited:	21 Apr 2016 09:56
Last Modified:	16 Dec 2022 12:56
DOI:	10.2140/agt.2007.7.327
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3000522