Remodeling a DS-diagram into one with E-cycle
type: Item
instance of: scholarly article
title: Remodeling a DS-diagram into one with E-cycle
zbMATH Open document ID: 0961.57018
author: Hiroshi Ikeda
author: Masakatsu Yamashita
author: Kazuo Yokoyama
published in: Tokyo Journal of Mathematics
publication date: 2000-10-30T00:00:00Z
review text: The paper is concerned with the combinatorial representation of compact 3-manifolds with boundary by standard spines [\textit{B. G. Casler}, Proc. Am. Math. Soc. 16, 559-566 (1965; Zbl 0129.15801)]. It is well known that two 3-manifolds are homeomorphic if and only if they have a standard spine in common. Subsequently, special classes of spines (called flow-spines) for closed 3-manifolds were constructed by using a flow on the manifold [\textit{I. Ishii}, Tokyo J. Math. 9, 505-525 (1986; Zbl 0697.57004)]. The authors give an algorithm to deform a standard spine to a flow-spine in a given closed 3-manifold. This algorithm is based on the theory of DS-diagrams which describe standard spines by graph-theoretical tools [see for example \textit{H. Ikeda} and \textit{Y. Inoue}, Kobe J. Math. 2, 169-185 (1985; Zbl 0602.57008)].
reviewed by: Alberto Cavicchioli
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 1523373
zbMATH Keywords: standard spine
zbMATH Keywords: flow-spine
zbMATH Keywords: 3-manifold
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1255958811
OpenAlex ID: W1992529278
DOI: 10.3836/TJM/1255958811
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description: scientific article; zbMATH DE number 1523373