The duality conjecture in formal knot theory
type: Item
instance of: scholarly article
title: The duality conjecture in formal knot theory
zbMATH Open document ID: 0591.57001
author: Patrick M. Gilmer
author: Richard A. Litherland
published in: Osaka Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The first three sections of this paper prove the following strengthened version of the duality conjecture arising in Kauffman's formal knot theory: the state polynomial \(<K>\) of a knot K is invariant under the involution of \({\mathbb{Z}}[B,W]\) which sends B to -W. The fourth section gives a new, simpler proof of the clock theorem of Kauffman, reformulating it as asserting that the set of maximal trees in a connected planar graph is a distributive lattice with respect to a naturally defined partial order.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 3949307
zbMATH Keywords: Reidemeister move
zbMATH Keywords: tangle
zbMATH Keywords: duality conjecture
zbMATH Keywords: formal knot theory
zbMATH Keywords: state polynomial
zbMATH Keywords: clock theorem
zbMATH Keywords: set of maximal trees in a connected planar graph
zbMATH Keywords: distributive lattice
reviewed by: Jonathan A. Hillman
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3949307