Knots with distinct primitive/primitive and primitive/Seifert representatives

Brandy Guntel Doleshal

doi:10.1142/s0218216511009625

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arXiv · 0909.0476

Knots with distinct primitive/primitive and primitive/Seifert representatives

Brandy Guntel Doleshal

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Abstract

Berge introduced knots that are primitive/primitive with respect to the genus 2 Heegaard surface, $F$, in $S^3$; surgery on such knots at the surface slope yields a lens space. Later Dean described a similar class of knots that are primitive/Seifert with respect to $F$; surgery on these knots at the surface slope yields a Seifert fibered space. Here we construct a two-parameter family of knots that have distinct primitive/Seifert embeddings in $F$ with the same surface slope, as well as a family of torus knots that have a primitive/primitive representative and a primitive/Seifert representative with the same surface slope.

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BibTeX RIS

Brandy Guntel Doleshal. 2015-05-20. Knots with distinct primitive/primitive and primitive/Seifert representatives. https://doi.org/10.1142/s0218216511009625

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