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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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: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3000522 |
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