Volume 7, issue 1 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Integrality of Homfly 1–tangle invariants

H R Morton

Algebraic & Geometric Topology 7 (2007) 327–338

arXiv: math.GT/0606336

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.

Keywords
Homfly, skein, annulus, quantum $sl(N)$, irreducible, integrality, 1–tangle
Mathematical Subject Classification 2000
Primary: 57M25, 57M27
Secondary: 57R56
References
Publication
Received: 18 December 2006
Accepted: 12 February 2007
Published: 29 March 2007
Authors
H R Morton
Department of Mathematical Sciences
University of Liverpool
Peach Street
Liverpool L69 7ZL
UK