On the additivity of \(h\)-genus of knots
type: Item
instance of: scholarly article
title: On the additivity of \(h\)-genus of knots
zbMATH Open document ID: 0826.57004
author: Kanji Morimoto
published in: Osaka Journal of Mathematics
publication date: 1994-09-15T00:00:00Z
review text: The \(h\)-genus of a knot \(K\) in \(S^3\) is the minimum genus \(h(K)\) of all Heegaard surfaces in \(S^3\) containing \(K\). Thus \(h(K)=1\) if and only if \(K\) is a (non-trivial) torus knot. The author shows that if the \(h\)-genus of a connected sum of two non-trivial knots \(K_1\), \(K_2\) is 2, then \(K_1\) and \(K_2\) are torus knots. On the other hand he gives examples to show that in general the \(h\)-genus is not additive with respect to connected sums.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 639566
zbMATH Keywords: \(h\)-genus of a knot
zbMATH Keywords: connected sum of two non-trivial knots
zbMATH Keywords: torus knots
reviewed by: Wolfgang Heil
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 639566