Satellite knots and L-space surgeries
نویسندگان
چکیده
منابع مشابه
Montesinos knots, Hopf plumbings and L-space surgeries
Using Hirasawa-Murasugi’s classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman-Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight contact structure on S. We also construct L-space knots with arbitrarily larg...
متن کاملLens space surgeries on A’Campo’s divide knots
It is proved that every knot in the major subfamilies of J. Berge’s lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped (real) plane curve as a divide knot defined by N. A’Campo in the context of singularity theory of complex curves. For each knot given by Berge’s parameters, the corresponding plane curve is constructed. The surgery coefficients ar...
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We describe necessary and sufficient conditions for a knot in an L-space to have an L-space homology sphere surgery. We use these conditions to reformulate a conjecture of Berge about which knots in S admit lens space surgeries.
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A 3-manifold is ∂-reducible if ∂M is compressible in M . By definition, this means that there is a disk D properly embedded in M so that ∂D is an essential curve in ∂M . The disk D is called a compressing disk of ∂M , or a ∂-reducing disk of M . Now suppose M is a ∂-reducible manifold. Let K be a knot in a 3-manifold M such that ∂M is incompressible in M − K. A Dehn surgery on K is called ∂-red...
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We classify Dehn surgeries on (p, q, r) pretzel knots resulting in a manifold M(α) having cyclic fundamental group and analyze those leading to a finite fundamental group. The proof uses the theory of cyclic and finite surgeries developed by Culler, Shalen, Boyer, and Zhang. In particular, CullerShalen seminorms play a central role.
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2016
ISSN: 0024-6093,1469-2120
DOI: 10.1112/blms/bdw044