Genus one cobordisms between torus knots

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.

arXiv comment20 pages, 12 figures. V3: Minor corrections and implementation of referee's recommendations. This version has been accepted for publication by IMRN

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Cited by in corpus (2)

• A note on the four-dimensional clasp number of knots
• Cobordism distance on the projective space of the knot concordance group