Invariants for Legendrian knots in lens spaces

Abstract

In this paper we define invariants for primitive Legendrian knots in lens spaces L(p,q) for q not equal to 1. The main invariant is a differential graded algebra which is computed from a labeled Lagrangian projection of the pair (L(p,q), K). This invariant is formally similar to a DGA defined by Sabloff which is an invariant for Legendrian knots in smooth S^1-bundles over Riemann surfaces. The second invariant defined for knots in lens spaces takes the form of a DGA enhanced with a free cyclic group action and can be computed from the p-fold cover of the pair (L(p,q), K).