Invariants for Legendrian knots in lens spaces

2009/01/27 by Joan E. Licata, Licata, Joan E. · 2 citations
Mathematics · #57M27 #57R17 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:57M27 #msc:57R17

paper · pdf · doi:10.48550/arxiv.0901.4226

25 pages, 18 figures

arxiv created 2009/01/27 · arxiv updated 2009/12/01

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 S¹-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).

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• Non-Simple knots in Contact 3-Manifolds
• Invariants of Legendrian knots in thickened convex surfaces

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