FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 4, PAGES 197-202

The algorithm of finding planar surfaces in three-manifolds

E. A. Sbrodova

Abstract

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By a slope in the boundary $$¶M of a $3$-manifold, we mean the isotopy class $$a of a finite set of disjoint simple closed curves in $$¶M which are nontrivial and pairwise nonparallel. In this paper, we construct an algorithm to decide whether or not a given orientable $3$-manifold $M$ contains an essential planar surface whose boundary has a given slope $$a.

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Last modified: November 29, 2005