Regular genus: the boundary case
type: Item
instance of: scholarly article
title: Regular genus: the boundary case
zbMATH Open document ID: 0618.57009
DOI: 10.1007/BF00147937
author: C. Gagliardi
published in: Geometriae Dedicata
publication date: 1987-01-01T00:00:00Z
review text: A particular kind of 2-cell imbedding for a class of edge-coloured graphs into surfaces with boundary is introduced and studied. This allows one to define, as in our earlier work [Proc. Am. Math. Soc. 81, 473-481 (1981; Zbl 0467.57004)], where the closed case was treated, a pair of invariants - the regular genus and the hole-number - for every n-manifold with boundary. These invariants are proved to coincide with the classical ones in dimension two, and to be strictly related with a Heegaard-like handlebody decomposition in dimension three. A characterization of \({\mathbb{D}}^ n\) concludes the work.
Mathematics Subject Classification ID: 57Q99
Mathematics Subject Classification ID: 57N15
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 4003076
zbMATH Keywords: manifold crystallization
zbMATH Keywords: Heegaard diagram
zbMATH Keywords: 2-cell imbedding
zbMATH Keywords: edge- coloured graphs
zbMATH Keywords: regular genus
zbMATH Keywords: hole-number
zbMATH Keywords: n-manifold with boundary
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4003076