An algorithm for finding planar surfaces in three-manifolds.

By a slope in the boundary ∂ M of a 3-manifold, we mean the isotopy class α of a finite set of disjoint simple closed curves in ∂ M that 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 α. [ABSTRACT FROM AUTHOR]