Compressing handlebodies with holes
type: Item
instance of: scholarly article
title: Compressing handlebodies with holes
zbMATH Open document ID: 0683.57004
DOI: 10.1016/0040-9383(89)90007-4
author: W. Menasco
author: Abigail Thompson
published in: Topology
publication date: 1989-01-01T00:00:00Z
review text: A theorem of Fox asserts that a 3-manifold M with connected boundary can be embedded in 3-space if and only if it is possible to glue 2-handles along the boundary of M so that the resulting manifold is a handlebody, namely can be cut along a family of disjoint embedded disks to obtain a 3-ball. The authors introduce a notion of handle-wormhole structure on M hich keeps track of this process of adding 2-handles and cutting along discs. The main result of the article is that, if M has compressible boundary, any handle-wormhole structure for M can be modified by a sequence of relatively simple moves so as to avoid a compression disk for \(\partial M\).
reviewed by: Francis Bonahon
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57R65
Mathematics Subject Classification ID: 57M35
zbMATH DE Number: 4119252
zbMATH Keywords: surfaces in 3-space
zbMATH Keywords: hollow handlebodies
zbMATH Keywords: Heegaard splittings
zbMATH Keywords: 3- manifold
zbMATH Keywords: handle-wormhole structure
zbMATH Keywords: adding 2-handles
zbMATH Keywords: cutting along discs
MaRDI profile type: Publication
full work available at URL: 0040-9383(89)90007-4
OpenAlex ID: W1975072578
description: scientific article; zbMATH DE number 4119252