Geodesic
The algorithm of finding planar surfaces in three-manifolds
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 197-202.

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By a slope in the boundary $\partial M$ of a 3-manifold, we mean the isotopy class $\alpha$ of a finite set of disjoint simple closed curves in $\partial M$ which are nontrivial and pairwise nonparallel. In this paper, we construct an algorithm to decide whether or not a given orientable 3-manifold $M$ contains an essential planar surface whose boundary has a given slope $\alpha$. 
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E. A. Sbrodova. The algorithm of finding planar surfaces in three-manifolds. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 197-202. http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a14/

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