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Matematicheskie Zametki, 2007, Volume 82, Issue 4, Pages 593–597
DOI: https://doi.org/10.4213/mzm4020 (Mi mzm4020) 		 
Algorithms for Finding Proper Essential Surfaces in 3-Manifolds

E. A. Sbrodovaab

a Chelyabinsk State University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
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DOI: https://doi.org/10.4213/mzm4020
Abstract: In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold $M$, verifies whether $M$ contains an essential orientable surface (possibly, with boundary), whose genus is at most $N$. The algorithm is based on Haken's theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold.
Keywords: irreducible 3-manifold, essential surface, boundary irreducible manifold, Euler characteristic, triangulation.
Received: 05.02.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 4, Pages 531–534
DOI: https://doi.org/10.1134/S0001434607090295
Bibliographic databases:
UDC: 515.16
Language: Russian
Citation: E. A. Sbrodova, “Algorithms for Finding Proper Essential Surfaces in 3-Manifolds”, Mat. Zametki, 82:4 (2007), 593–597; Math. Notes, 82:4 (2007), 531–534
Citation in format AMSBIB
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