\(H'\)-splittings of Seifert manifolds with boundary
type: Item
instance of: scholarly article
title: \(H'\)-splittings of Seifert manifolds with boundary
zbMATH Open document ID: 1518.57023
publication date: 2023-06-07T00:00:00Z
review text: Heegaard splittings of \(3\)-manifolds are an important topic in low dimensional topology, and play an important role in the study of \(3\)-manifolds. \(H'\)-splittings of \(3\)-manifolds are a generalization of Heegaard splittings to \(3\)-manifolds with boundaries. It is known that each compact connected orientable \(3\)-manifold with boundary admits an \(H'\)-splitting. In the paper under review, the authors study \(H'\)-splittings of Seifert manifolds with boundaries, and prove that a non-completely \(L\)-reducible and minimal \(H'\)-splitting surface for a compact connected irreducible orientable anannular Seifert \(3\)-manifold with boundary is horizontal. Also, the authors give a necessary and sufficient condition for an amalgamation of two compact connected orientable \(3\)-manifolds along a compact connected surface to be a Seifert manifold with boundary.
reviewed by: Kun Du
Mathematics Subject Classification ID: 57K30
zbMATH DE Number: 7693486
zbMATH Keywords: Seifert manifold
zbMATH Keywords: \(H'\)-splitting
zbMATH Keywords: vertical or horizontal surface
zbMATH Keywords: amalgamated 3-manifold
MaRDI profile type: Publication
cites work: Genus 2 Heegaard decompositions of small Seifert manifolds
cites work: Weakly reducible H′-splittings of 3-manifolds
cites work: Fundamental groups of 3-manifolds which are extensions
cites work: Q3871581
cites work: A necessary and sufficient condition for a surface sum of two handlebodies to be a handlebody
cites work: Heegaard splittings of Seifert fibered spaces
cites work: Irreducible Heegaard splittings of Seifert fibered spaces are either vertical or horizontal
cites work: Q3726998
cites work: The Classification of Heegaard Splittings for (Compact Orient Able Surface) × S1
cites work: Heegaard Splittings of Seifert Fibered Spaces with Boundary
cites work: Q4950141
cites work: Semibundle decomposition of 3-manifolds and the twisted cofundamental group
cites work: Seifert 3-manifolds that are bundles and semi-bundles
DOI: 10.1007/S10114-023-2203-X
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 7693486