Some remarks on cabling, contact structures, and complex curves

Details Some remarks on cabling, contact structures, and complex curves Some remarks on cabling, contact structures, and complex curves

2008-04-28

arxiv.org/abs/0804.4327v1

Mathematics

Geometric Topology

11 pages, 1 figure. This paper will appear in the Proceedings of the 2007 Gokova Geometry and Topology conference

Scientific paper

We determine the relationship between the contact structure induced by a fibered knot, K, in the three-sphere and the contact structures induced by its various cables. Understanding this relationship allows us to classify fibered cable knots which bound a properly embedded complex curve in the four-ball satisfying a genus constraint. This generalizes the well-known classification of links of plane curve singularities.

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