Journal article

FINDING PLANAR SURFACES IN KNOT- AND LINK-MANIFOLDS

William Jaco, J Hyam Rubinstein, Eric Sedgwick

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | WORLD SCIENTIFIC PUBL CO PTE LTD | Published : 2009

Abstract

It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface; if it does, the algorithm will construct one. Two similar results are obtained with added boundary conditions. Namely, given a link-manifold M, a component B of ∂M, and a slope γ on B, there is an algorithm to decide if there is an embedded punctured-disk in M with boundary γ and punctures in ∂M\B; and given a link-manifold M, a component B of ∂M, and a meridian slope μ on B, there is an algorithm to decide if there is an embedded punctured-disk with boundary a longitude on B and punctures in ∂M\B. In both cases, if there is one, the algorithm will constru..

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