A spanning tree expansion of the Jones polynomial
type: Item
instance of: scholarly article
title: A spanning tree expansion of the Jones polynomial
zbMATH Open document ID: 0622.57003
DOI: 10.1016/0040-9383(87)90003-6
author: Morwen Thistlethwaite
published in: Topology
publication date: 1987-01-01T00:00:00Z
review text: This paper presents a reformulation of the bracket polynomial of Kauffman (and hence of the Jones polynomial) for an oriented link, based on ideas related to the Tutte polynomial of graph theory. The bracket polynomial is expressed as a sum of monomials, indexed by the set of spanning trees of the graph associated with a black-and-white colouring of the regions of a link diagram. Some interesting connections between the crossing number of alternating link diagrams and the reduced degree (''breadth'') of the Jones polynomial (also observed in part by Kauffman and by Murasugi) follow from this approach.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4009330
zbMATH Keywords: bracket polynomial
zbMATH Keywords: Jones polynomial
zbMATH Keywords: oriented link
zbMATH Keywords: Tutte polynomial
zbMATH Keywords: crossing number of alternating link diagrams
reviewed by: Jonathan A. Hillman
MaRDI profile type: Publication
full work available at URL: 0040-9383(87)90003-6
OpenAlex ID: W2068033618
Wikidata QID: Q56456437
description: scientific article; zbMATH DE number 4009330