On the Heegaard genus and tri-genus of non-orientable Seifert 3-manifolds
type: Item
instance of: scholarly article
title: On the Heegaard genus and tri-genus of non-orientable Seifert 3-manifolds
zbMATH Open document ID: 0940.57023
DOI: 10.1016/S0166-8641(98)00110-2
author: Víctor Núñez
published in: Topology and its Applications
publication date: 2000-02-08T00:00:00Z
review text: The author computes several geometric invariants of Seifert fiber spaces. He does not assume that the Seifert fiber spaces are orientable. He considers the Heegaard genus, the tri-genus and the minimal genus representation of a given homology class. The Heegaard genus is a well-known invariant. It is a fact that any 3-manifold (orientable or not) may be expressed as the union of three orientable handlebodies. The genera of the three handlebodies ordered lexicographically is known as the tri-genus. The author computes what is essentially the minimal genus of a surface dual to the first Stiefel-Whitney class. He also computes the minimal genus of a fiber, for those Seifert manifolds which fiber over a circle. The rank of \(\pi_1(M)/\langle h\rangle\) is a good lower bound for the genus of a Seifert fiber space. This leads to the Heegaard genus of all but a few Seifert fiber spaces. There is a vertical torus dual to the first Stiefel-Whitney class of a Seifert fiber space. This is the basis for the computation of the Stiefel-Whitney genus. The fibers of a fibration over \(S^1\) are analyzed by projecting to the base orbifold of the Seifert manifold. He studies the vertical torus dual to the Stiefel-Whitney class in order to compute the tri-genus.
reviewed by: David Auckly
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M27
zbMATH DE Number: 1367566
zbMATH Keywords: Seifert manifolds
MaRDI profile type: Publication
full work available at URL: s0166-8641(98)00110-2
OpenAlex ID: W1999843703
description: scientific article; zbMATH DE number 1367566