One-sided incompressible surfaces in Seifert fibered spaces
type: Item
instance of: scholarly article
title: One-sided incompressible surfaces in Seifert fibered spaces
zbMATH Open document ID: 0606.57007
DOI: 10.1016/0166-8641(86)90032-5
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: In his thesis [Invent. Math. 3, 308-333, and 4, 87-117 (1967; Zbl 0168.445)], \textit{F. Waldhausen} classified the two-sided incompressible surfaces in Seifert 3-manifolds, by showing that each of them was isotopic either to a ''vertical'' surface (union of fibers of the Seifert fibration) or to a ''horizontal'' surface (transverse to the fibration). In the present paper, the author carries out a similar analysis for one- sided incompressible surfaces in Seifert manifolds. More precisely, he shows that each one-sided incompressible surface is isotopic to either a ''pseudovertical'' or a ''pseudohorizontal'' surface, namely one which is vertical or horizontal outside of a tubular neighborhood of some fibers. Conversely, he also proves that pseudovertical surfaces are incompressible, and gives an isotopy classification of these pseudovertical surfaces. The general problem of classifying pseudohorizontal surfaces remains open.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57N35
Mathematics Subject Classification ID: 57N37
zbMATH DE Number: 3980031
zbMATH Keywords: one-sided incompressible surfaces in Seifert manifolds
author: Charles Frohman
reviewed by: Francis Bonahon
MaRDI profile type: Publication
full work available at URL: 0166-8641(86)90032-5
OpenAlex ID: W2041705666
cites work: Non-orientable surfaces in orientable 3-manifolds
cites work: Q3871581
cites work: Q4185506
cites work: One-sided Heegaard splittings of 3-manifolds
cites work: Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I, II
cites work: On irreducible 3-manifolds which are sufficiently large
description: scientific article; zbMATH DE number 3980031