On the knot Floer homology of twisted torus knots

Abstract

In this paper we study the knot Floer homology of a subfamily of twisted $(p,q)$ torus knots where $q\equiv \pm 1$ (mod $p$). Specifically, we classify the knots in this subfamily that admit L-space surgeries. To do calculations, we use the fact that these knots are $(1,1)$ knots and, therefore, admit a genus one Heegaard diagram.

17 pages, 12 figures; v2: minor revisions throughout

References in corpus (1)

• Berge-Gabai knots and L-space satellite operations

Cited by in corpus (11)

• Floer Simple Manifolds and L-Space Intervals
• (1,1) L-space knots
• Berge-Gabai knots and L-space satellite operations
• L-space surgery and twisting operation
• Heegaard Floer homology of L-space links with two components
• Taut Foliations, Positive 3-Braids, and the L-Space Conjecture
• Unexpected Essential Surfaces among Exteriors of Twisted Torus Knots
• Twist positivity, L-space knots, and concordance
• Taut foliations, braid positivity, and unknot detection
• The Alexander polynomial of twisted torus knots
• New family of hyperbolic knots whose Upsilon invariants are convex