In this paper, we introduce a rational $tau$ invariant for rationally null-homologous knots in contact 3-manifolds with nontrivial Ozsv{a}th-Szab{o} 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.
Download