A bound for rational Thurston-Bennequin invariants

Abstract

In this paper, we introduce a rational $\tau$ invariant for rationally null-homologous knots in contact 3-manifolds with nontrivial Ozsváth-Szabó contact invariants. Such an invariant is an upper bound for the sum of rational Thurston-Bennequin invariant and the rational rotation number of the Legendrian representatives of the knot. In the special case of Floer simple knots in L-spaces, we can compute the rational $\tau$ invariants by correction terms.

16 pages, 2 figures

References in corpus (3)

• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• $\tau$-invariants for knots in rational homology spheres
• Null surgery on knots in L-spaces