A necessary and sufficient condition for a 3-manifold to have genus \(g\) Heegaard splitting (a proof of Hass-Thompson conjecture)
type: Item
instance of: scholarly article
title: A necessary and sufficient condition for a 3-manifold to have genus \(g\) Heegaard splitting (a proof of Hass-Thompson conjecture)
zbMATH Open document ID: 0822.57014
author: Tsuyoshi Kobayashi
author: Haruko Nishi
published in: Osaka Journal of Mathematics
publication date: 1995-10-17T00:00:00Z
review text: The condition referred to in the title is that there exist a genus \(g\) handlebody in the manifold such that any knot in the manifold can be ambient isotoped to lie inside the handlebody. The genus 0 case was obtained by \textit{R. H. Bing} [Ann. Math., II. Ser. 68, 17-37 (1958; Zbl 0081.392)] and the genus 1 case by \textit{J. Hass} and \textit{A. Thompson} [Proc. Am. Math. Soc. 107, No. 4, 1107-1110 (1989; Zbl 0694.57006)].
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 639567
zbMATH Keywords: Heegard splitting
zbMATH Keywords: genus
zbMATH Keywords: 3-manifold
zbMATH Keywords: knot
reviewed by: Lee P. Neuwirth
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 639567