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Sbornik: Mathematics, 1998, Volume 189, Issue 10, Pages 1517–1531
DOI: https://doi.org/10.1070/sm1998v189n10ABEH000352 (Mi sm352) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Generalized graph manifolds and their effective recognition

S. V. Matveev

Chelyabinsk State University
English version PDF (209 kB) Citations (3)
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DOI: https://doi.org/10.1070/sm1998v189n10ABEH000352
Abstract: A generalized graph manifold is a three-dimensional manifold obtained by gluing together elementary blocks, each of which is either a Seifert manifold or contains no essential tori or annuli. By a well-known result on torus decomposition each compact three-dimensional manifold with boundary that is either empty or consists of tori has a canonical representation as a generalized graph manifold. A short simple proof of the existence of a canonical representation is presented and a (partial) algorithm for its construction is described. A simple hyperbolicity test for blocks that are not Seifert manifolds is also presented.
Received: 25.05.1998
Russian version:
Matematicheskii Sbornik, 1998, Volume 189, Number 10, Pages 89–104
DOI: https://doi.org/10.4213/sm352
Bibliographic databases:
UDC: 513.83
MSC: Primary 57N10; Secondary 57-04
Language: English
Original paper language: Russian
Citation: S. V. Matveev, “Generalized graph manifolds and their effective recognition”, Mat. Sb., 189:10 (1998), 89–104; Sb. Math., 189:10 (1998), 1517–1531
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:13
    References:56
    First page:2
     
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