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    FINDING PLANAR SURFACES IN KNOT- AND LINK-MANIFOLDS

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    Author
    Jaco, W; Rubinstein, JH; Sedgwick, E
    Date
    2009-03-01
    Source Title
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
    Publisher
    WORLD SCIENTIFIC PUBL CO PTE LTD
    University of Melbourne Author/s
    Rubinstein, Joachim
    Affiliation
    Mathematics and Statistics
    Metadata
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    Document Type
    Journal Article
    Citations
    Jaco, W., Rubinstein, J. H. & Sedgwick, E. (2009). FINDING PLANAR SURFACES IN KNOT- AND LINK-MANIFOLDS. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 18 (3), pp.397-446. https://doi.org/10.1142/S0218216509006987.
    Access Status
    This item is currently not available from this repository
    URI
    http://hdl.handle.net/11343/29232
    DOI
    10.1142/S0218216509006987
    Abstract
    <jats:p> 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 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. </jats:p>
    Keywords
    Pure Mathematics

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