On primitive sets of loops in the boundary of a handlebody
type: Item
instance of: scholarly article
title: On primitive sets of loops in the boundary of a handlebody
zbMATH Open document ID: 0634.57007
DOI: 10.1016/0166-8641(87)90093-9
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: It is shown that a collection \(\{J_ 1,J_ 2,...\}\) of pairwise disjoint simple closed curves in the boundary of a 3-dimensional handlebody, X, is primitive if and only if for each subcollection of the curves the 3-manifold obtained by attaching 2-handles to X along the curves of the subcollection is a handlebody. Being primitive means that there is a collection \(\{D_ 1,D_ 2,...\}\) of pairwise disjoint, properly embedded 2-cells in X which are transverse to \(\{J_ 1,J_ 2,...\}\) and with \(| J_ i\cap D_ j| =\delta_{ij}\).
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57N05
zbMATH DE Number: 4032623
zbMATH Keywords: pairwise disjoint simple closed curves in the boundary of a 3-dimensional handlebody
zbMATH Keywords: attaching 2-handles
author: Cameron McA. Gordon
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90093-9
OpenAlex ID: W2111643160
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description: scientific article; zbMATH DE number 4032623