Obstructions to Lagrangian concordance

Cornwell, Christopher¹ ; Ng, Lenhard² ; Sivek, Steven³

¹CIRGET, Université du Québec à Montréal, CP 8888 Succursale Centre-ville, Montréal H3C 3P8, Canada
²Department of Mathematics, Duke University, Box 90320, Durham, NC 27708-0320, USA
³Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA

Algebraic and Geometric Topology, Tome 16 (2016) no. 2, pp. 797-824

Résumé

We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in ℝ3. In particular, we give obstructions to a concordance from an arbitrary knot to the standard Legendrian unknot, in terms of normal rulings. We also place strong restrictions on knots that have concordances both to and from the unknot and construct an infinite family of knots with nonreversible concordances from the unknot. Finally, we use our obstructions to present a complete list of knots with up to 14 crossings that have Legendrian representatives that are Lagrangian  slice.

Détail

DOI : 10.2140/agt.2016.16.797

Classification : 57M25, 57R17, 53D42, 53D12
Keywords: Legendrian knots, Lagrangian concordance

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