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2007 Integrality of Homfly 1–tangle invariants
H R Morton
Algebr. Geom. Topol. 7(1): 327-338 (2007). DOI: 10.2140/agt.2007.7.327

Abstract

Given an invariant J(K) of a knot K, the corresponding 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 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 then J is always an integer 2–variable Laurent polynomial. Specialisation of the 2–variable polynomials for suitable choices of eigenvector shows that the 1–tangle irreducible quantum sl(N) invariants of K are integer 1–variable Laurent polynomials.

Citation

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H R Morton. "Integrality of Homfly 1–tangle invariants." Algebr. Geom. Topol. 7 (1) 327 - 338, 2007. https://doi.org/10.2140/agt.2007.7.327

Information

Received: 18 December 2006; Accepted: 12 February 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1132.57014
MathSciNet: MR2308948
Digital Object Identifier: 10.2140/agt.2007.7.327

Subjects:
Primary: 57M25, 57M27
Secondary: 57R56

Rights: Copyright © 2007 Mathematical Sciences Publishers

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