Dehn surgery on arborescent knots
type: Item
instance of: scholarly article
title: Dehn surgery on arborescent knots
zbMATH Open document ID: 0851.57018
author: Ying-Qing Wu
published in: Journal of Differential Geometry
publication date: 1996-07-01T00:00:00Z
review text: A knot \(K\) is called an arborescent knot if it can be obtained by summing and gluing several rational tangles together; see [\textit{D. Gabai}, Mem. Am. Math. Soc. 339, 1-98 (1986; Zbl 0585.57003)] for more detailed definitions. Recall that a 3-manifold is called a Haken manifold if it is irreducible and contains an incompressible surface. Following \textit{A. Hatcher} [Ann. Inst. Fourier 42, 313-325 (1992; Zbl 0759.57006)] we say that a 3-manifold \(M\) is laminar if it contains an essential lamination. The purpose of this paper is to study Dehn surgeries on arborescent knots, and to see which of these surgered manifolds are laminar, Haken, or hyperbolic.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 895021
zbMATH Keywords: arborescent knot
zbMATH Keywords: rational tangles
zbMATH Keywords: 3-manifold
zbMATH Keywords: Haken manifold
zbMATH Keywords: essential lamination
zbMATH Keywords: hyperbolic
Wikidata QID: Q115177771
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214457901
OpenAlex ID: W1587435702
DOI: 10.4310/JDG/1214457901
description: scientific article; zbMATH DE number 895021