Celebratio Mathematica — Rubinstein

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Works connected to Eric David Sedgwick

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W. Jaco, J. H. Rubinstein, and E. Sedgwick: “Finding planar surfaces in knot- and link-manifolds,” J. Knot Theory Ramifications 18 : 3 (2009), pp. 397–446. MR 2514851 Zbl 1176.57024 ArXiv 0608700 article

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 \( \partial M \), and a slope \( \gamma \) on \( B \), there is an algorithm to decide if there is an embedded punctured-disk in \( M \) with boundary \( \gamma \) and punctures in \( \partial M\backslash B \); and given a link-manifold \( M \), a component \( B \) of \( \partial M \), and a meridian slope \( \mu \) on \( B \), there is an algorithm to decide if there is an embedded punctured-disk with boundary a longitude on \( B \) and punctures in \( \partial M\backslash B \). In both cases, if there is one, the algorithm will construct one. The proofs introduce a number of new methods and differ from the classical proofs, using normal surfaces, as solutions may not be found among the fundamental solutions.

William H. Jaco	Related
Eric David Sedgwick	Related