Rational Seifert Surfaces in Seifert Fibered Spaces

Joan E. Licata; Joshua M. Sabloff

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arXiv · 1108.2182

Rational Seifert Surfaces in Seifert Fibered Spaces

Joan E. Licata·Joshua M. Sabloff

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Abstract

Rationally null-homologous links in Seifert fibered spaces may be represented combinatorially via labeled diagrams. We introduce an additional condition on a labeled link diagram and prove that it is equivalent to the existence of a rational Seifert surface for the link. In the case when this condition is satisfied, we generalize Seifert's algorithm to explicitly construct a rational Seifert surface for any rationally null-homologous knot. As an application of the techniques developed in the paper, we derive closed formulae for the rational Thurston-Bennequin and rotation numbers of a Legendrian knot in a contact Seifert fibered space.

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BibTeX RIS

Joan E. Licata, Joshua M. Sabloff. 2011-08-10. Rational Seifert Surfaces in Seifert Fibered Spaces. https://arxiv.org/abs/1108.2182

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