A family of transversely nonsimple knots

Abstract

We apply knot Floer homology to exhibit an infinite family of transversely nonsimple prime knots starting with $10_{132}$. We also discuss the combinatorial relationship between grid diagrams, braids, and Legendrian and transverse knots in standard contact ${\mathbb{R}}^3$.

19 pages, v2: minor corrections to statements in section 2.4

References in corpus (3)

• Legendrian knots, transverse knots and combinatorial Floer homology
• Transversely non simple knots
• Connect sum and transversely non simple knots

Cited by in corpus (9)

• Combinatorial knot contact homology and transverse knots
• An atlas of Legendrian knots
• On the equivalence of Legendrian and transverse invariants in knot Floer homology
• Transverse invariants and right-veering
• On the equivalence of contact invariants in sutured Floer homology theories
• An annular refinement of the transverse element in Khovanov homology
• Comultiplication in link Floer homology and transversely non-simple links
• Grid diagram for singular links
• Obstruction Complexes in Grid Homology