Genus one cobordisms between torus knots

Peter Feller; JungHwan Park

doi:10.1093/imrn/rnaa027

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arXiv · 1910.01672

Genus one cobordisms between torus knots

Peter Feller·JungHwan Park

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Abstract

We determine the pairs of torus knots that have a genus one cobordism between them, with one notable exception. This is done by combining obstructions using $\nu^+$ from the Heegaard Floer knot complex and explicit constructions of cobordisms. As an application, we determine the pairs of torus knots related by a single crossing change. Also, we determine the pairs of Thurston-Bennequin number maximizing Legendrian torus knots that have a genus one exact Lagrangian cobordism, with one exception.

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BibTeX RIS

Peter Feller, JungHwan Park. 2019-10-03. Genus one cobordisms between torus knots. https://doi.org/10.1093/imrn%2Frnaa027

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