Orbi-maps and 3-orbifolds
type: Item
instance of: scholarly article
title: Orbi-maps and 3-orbifolds
zbMATH Open document ID: 0704.57006
author: Yoshihiro Takeuchi
published in: Proceedings of the Japan Academy. Series A
publication date: 1989-01-01T00:00:00Z
review text: The author announces three theorems on 3-orbifolds which mimic well-known results of 3-manifold topology. Let M and N be compact, ``good'' 3- orbifolds (i.e. orbit spaces of 3-manifolds with respect to properly discontinuous group actions). The first theorem is on representing a homomorphism \(\pi_ 1M\to \pi_ 1N\) by an orbi-map (a concept defined in this paper) \(M\to N\), the second one is on approximating an orbi-map \(M\to N\) by one which is transverse to a 2-suborbifold of N, and the third one is on representing an isomorphism \(\pi_ 1M\to \pi_ 1N\) by an orbi-isomorphism \(M\to N\). Two applications to links and tangles are included.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4155457
zbMATH Keywords: representing homomorphisms between fundamental groups by orbi-maps
zbMATH Keywords: 3- orbifolds
zbMATH Keywords: orbit spaces of 3-manifolds
zbMATH Keywords: properly discontinuous group actions
zbMATH Keywords: approximating an orbi-map
zbMATH Keywords: transverse to a 2-suborbifold
zbMATH Keywords: orbi- isomorphism
reviewed by: Joze Vrabec
MaRDI profile type: Publication
full work available at URL: pjaa.65.345
OpenAlex ID: W1996680978
cites work: Hierarchies for 3-orbifolds
cites work: Q4114528
cites work: ON A GENERALIZATION OF THE NOTION OF MANIFOLD
cites work: On irreducible 3-manifolds which are sufficiently large
cites work: Some groups which classify knots
cites work: The \(\pi\)-orbifold group of a link
DOI: 10.3792/PJAA.65.345
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description: scientific article; zbMATH DE number 4155457