Some remarks on cabling, contact structures, and complex curves

Matthew Hedden

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arXiv · 0804.4327

Some remarks on cabling, contact structures, and complex curves

Matthew Hedden

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Abstract

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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Matthew Hedden. 2008-04-28. Some remarks on cabling, contact structures, and complex curves. https://arxiv.org/abs/0804.4327

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