A proof of Przytycki's conjecture on \(n\)-relator 3-manifolds
type: Item
instance of: scholarly article
title: A proof of Przytycki's conjecture on \(n\)-relator 3-manifolds
zbMATH Open document ID: 0856.57013
DOI: 10.1016/0040-9383(95)93238-3
published in: Topology
publication date: 1997-02-04T00:00:00Z
review text: Let \(H\) be a 3-dimensional handlebody (possibly nonorientable) and \(C\) be a twosided closed 1-manifold in \(\partial H\) such that \(\partial H - C\) is incompressible in \(H\). Denote by \(H_C\) the 3-manifold obtained by attaching 2-handles to \(H\) along the components of \(C\). \textit{J. H. Przytycki} [Lond. Math. Soc. Lect. Note Ser. 112, 273-285 (1986; Zbl 0621.57005)] proposed a set of conditions on \(C\) which he conjectured to imply that \(H_C\) has incompressible boundary (or is a 3-ball); the conditions are purely algebraic and concern the homotopy classes of the components of \(C\) in \(\pi_1 (H)\). Przytycki himself verified his conjecture for \(C\) with no more than three components. In the present paper the author proves the conjecture in general.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57R65
zbMATH DE Number: 751258
zbMATH Keywords: 3-dimensional handlebody
zbMATH Keywords: 3-manifold
zbMATH Keywords: 2-handles
zbMATH Keywords: incompressible boundary
Wikidata QID: Q123195439
author: Fengchun Lei
reviewed by: Joze Vrabec
MaRDI profile type: Publication
full work available at URL: 0040-9383(95)93238-3
OpenAlex ID: W1977882477
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description: scientific article; zbMATH DE number 751258