A bound for rational Thurston-Bennequin invariants

2017/05/26 by Li, Youlin, Wu, Zhongtao · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1705.09440

Abstract

In this paper, we introduce a rational τ 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 τ invariants by correction terms.

Cited by

• Relative Thom Conjectures, symplectic and beyond

Related

• Rational linking and contact geometry
• An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold
• On the additivity of the Thurston--Bennequin invariant of Legendrian knots
• A New Way to Compute the Thurston-Bennequin Number
• Classical invariants of Legendrian knots in the 3-dimensional torus