On the slice-ribbon conjecture for Montesinos knots

By Ana G. Lecuona. 2009

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We establish the slice-ribbon conjecture for a family P of Montesinos knots by means of Donaldson’s theorem on the intersection forms of definite 4-manifolds. The 4-manifolds that we consider are obtained by plumbing disc bundles over S2 according to a star-shaped negative-weighted graph with 3 legs such that: i) the central vertex has weight less than or equal to −3; ii) − total weight − 3 #vertices < −1. The Seifert spaces which bound these 4-dimensional plumbing manifolds are the double covers of S3 branched along the Montesinos knots in the family P.

Subfields: Genetics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ea47a4a60efeea1967157f2d50d8320d3885736d

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In Genetics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Grid Homology for Knots and Links (2015, background): “The conjecture has been verified for 2-bridge knots [124] and for certain Montesinos knots [116], but it is open in general.”