Cyclic Dehn surgery and the A-polynomial
type: Item
instance of: scholarly article
title: Cyclic Dehn surgery and the A-polynomial
zbMATH Open document ID: 0963.57009
DOI: 10.1016/S0166-8641(99)00117-0
author: Patrick D. Shanahan
published in: Topology and its Applications
publication date: 2001-06-24T00:00:00Z
review text: The author investigates Dehn surgery on a knot in \(S^3\), i.e., the space resulting from sewing a solid torus along the boundary of a deleted regular neighborhood of a knot. The author applies a knot invariant introduced by \textit{D. Cooper, M. Culler, H. Gillet, D. D. Long} and \textit{P. B. Shalen} [Invent. Math. 118, No. 1, 47-84 (1994; Zbl 0842.57013)] called the \(A\)-polynomial. The main result provides a necessary condition for Dehn surgery to be cyclic. It is based on the width of the Newton polygon of the \(A\)-polynomial. The width produces a list of at most three slopes for a hyperbolic knot which contains no closed surface in its complement.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1538672
zbMATH Keywords: Newton polygon
zbMATH Keywords: knot
zbMATH Keywords: cyclic knot
reviewed by: Leonard R. Rubin
MaRDI profile type: Publication
full work available at URL: s0166-8641(99)00117-0
OpenAlex ID: W1964680637
Recommended article: DEHN SURGERY AND A-POLYNOMIAL FOR KNOTS
Recommended article: Variation of the Alexander-Conway polynomial under Dehn surgery
Recommended article: Dehn surgeries and rational homology balls
Recommended article: Q4234986
Recommended article: Dehn surgery and Seifert surface systems
Recommended article: Q4343785
Recommended article: Dehn surgeries on periodic links
Recommended article: Dehn surgery and nonseparating two-spheres
Recommended article: Dehn surgery on arborescent knots
Recommended article: Surgery, polygons and SU(N)‐Floer homology
description: scientific article; zbMATH DE number 1538672