Quasipositive pretzels
type: Item
instance of: scholarly article
title: Quasipositive pretzels
zbMATH Open document ID: 0974.57006
DOI: 10.1016/S0166-8641(00)00051-1
author: L. Rudolph
published in: Topology and its Applications
publication date: 2001-12-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/9908028
review text: A {quasipositive} surface in \(S^3\) is a surface which is generated from a 2-disk \(D^2\) by plumbing positive Hopf annuli \(A(0,-1)\) and passing to \(\pi_1\)-injective subsurfaces. In some sense, quasipositive surfaces are analogues in \(S^3\) of pieces of complex plane curve in \(D^4\subset C^2\). The notion of quasipositivity has been introduced by the author and explored in several of his previous papers. In this paper, he gives a necessary and sufficient condition for an oriented pretzel surface to be quasipositive. From this condition, he obtains an estimate for the slice genus of the boundary of an oriented pretzel surface.
reviewed by: Athanase Papadopoulos
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1624910
zbMATH Keywords: pretzel
zbMATH Keywords: braizel
zbMATH Keywords: quasipositivity
zbMATH Keywords: Seifert surface
zbMATH Keywords: slice genus
MaRDI profile type: Publication
arXiv ID: math/9908028
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description: scientific article; zbMATH DE number 1624910