| We define relative analogues of the classical Legendrian knot invariants for knots in a tight contact 3-manifold (M, ξ). We prove that the relative Thurston-Bennequin invariant is bounded above and we prove an extended and a relative Thurston-Bennequin inequality. We prove that the relative invariants are additive under various versions of Legendrian connected sums. Finally, we use the relative invariants to classify knots which cobound an annulus with the core in (S1 × D2, ξn), n < 0; and generalize this to any tight contact 3-manifold. |
