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INVARIANTS FOR LEGENDRIAN KNOTS IN LENS SPACES
- JOAN E. LICATA
Communications in Contemporary Mathematics01 Feb 2011
Preview Abstract
In this paper, we define invariants for primitive Legendrian knots in lens spaces L(p, q), q ≠ 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 S¹-bundles over Riemann surfaces. The second invariant defined for K ⊂ L(p, q) takes the form of a DGA enhanced with a free cyclic group action and can be computed from a cyclic cover of the pair (L(p, q), K).

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