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.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 197–202, 2005.
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Sbrodova, E.A. An algorithm for finding planar surfaces in three-manifolds. J Math Sci 144, 4500–4503 (2007). https://doi.org/10.1007/s10958-007-0288-x
- Planar Surface
- Euler Characteristic
- Isotopy Class
- Regular Neighborhood
- Puncture Sphere