Geodesic
Planar surfaces in three-manifolds
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 451-463 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we consider the problem of algorithmic finding of a proper essential planar surface in a given irreducible orientable compact $3$-manifold. The method uses the Haken theory of normal surfaces in $3$-manifolds with boundary pattern [5]. The solution is based on an estimate, considered in [3], of the average length of boundary curves of an arbitrary proper essential planar surface and on the notion of a slope in the boundary of an arbitrary manifold that generalizes the notion of a slope on a torus. 
@article{SEMR_2006_3_a29,
     author = {E. A. Sbrodova},
     title = {Planar surfaces in three-manifolds},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {451--463},
     year = {2006},
     volume = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2006_3_a29/}
}
TY  - JOUR
AU  - E. A. Sbrodova
TI  - Planar surfaces in three-manifolds
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2006
SP  - 451
EP  - 463
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/SEMR_2006_3_a29/
LA  - ru
ID  - SEMR_2006_3_a29
ER  - 
%0 Journal Article
%A E. A. Sbrodova
%T Planar surfaces in three-manifolds
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2006
%P 451-463
%V 3
%U http://geodesic.mathdoc.fr/item/SEMR_2006_3_a29/
%G ru
%F SEMR_2006_3_a29
E. A. Sbrodova. Planar surfaces in three-manifolds. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 3 (2006), pp. 451-463. http://geodesic.mathdoc.fr/item/SEMR_2006_3_a29/

[1] W. Haken, “Theorie der Normalflächen”, Acta Math., German, 105 (1961), 245–375 | MR | Zbl

[2] W. Jaco and U. Oertel, “An algorithm to decide if a 3-manifold is a Haken manifold”, Topology, 23:2 (1984), 195–209 | DOI | MR | Zbl

[3] W. Jaco, J. H. Rubinstein and E. Sedgwick, Finding planar surfaces in knot- and link-manifolds, arXiv: math/0608700 | MR

[4] W. Jaco and E. Sedgwick, Decision problems in the space of Dehn fillings, arXiv: math/9811031 | MR

[5] S. Matveev, Algorithmic Topology and Classification of 3-Manifolds, Springer-Verlag, Berlin, Heidelberg, 2003 | MR

[6] E. A. Sbrodova, “Algoritm nakhozhdeniya ploskikh poverkhnostei v trekhmernykh mnogoobraziyakh”, Fundamentalnaya i prikladnaya matematika, 11:4 (2005), 197–202 | MR