The realization of the decompositions of the 3-orbifold groups along the spherical 2-orbifold groups
type: Item
instance of: scholarly article
title: The realization of the decompositions of the 3-orbifold groups along the spherical 2-orbifold groups
zbMATH Open document ID: 1025.57004
DOI: 10.1016/S0166-8641(01)00241-3
author: Yoshihiro Takeuchi
author: Misako Yokoyama
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: It is a classical theorem of J. H. C. Whitehead that, subject to some minor conditions, if a fundamental group of a 3-manifold is a free product, then the 3-manifold is a connected sum -- that a decomposition as a free product at the group level can be realized by a decomposition at the manifold level. The authors extend this result as far as possible from 3-manifolds to 3-orbifolds. Their basic group-theoretic condition is that the fundamental 3-orbifold group should be a nontrivial free product with amalgamation over an orientable and spherical 2-orbifold group. The authors then prove that, except for very rare exceptions, there exists a spherical 2-suborbifold which realizes the decomposition geometrically. By example, they show that one of their rare exceptions actually occurs and that, in that case, the given group-theoretic decomposition cannot be realized geometrically.
Mathematics Subject Classification ID: 57M05
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57M60
Mathematics Subject Classification ID: 57M35
zbMATH DE Number: 1879086
zbMATH Keywords: orbifold fundamental group
zbMATH Keywords: 3-orbifold
zbMATH Keywords: amalgamated free product
reviewed by: James W. Cannon
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1879086