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Obstructions to Lagrangian concordance

Christopher Cornwell, Lenhard Ng and Steven Sivek

Algebraic & Geometric Topology 16 (2016) 797–824

We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in 3. 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.

Legendrian knots, Lagrangian concordance
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57R17, 53D42, 53D12
Received: 26 November 2014
Revised: 6 July 2015
Accepted: 15 July 2015
Published: 26 April 2016
Christopher Cornwell
CIRGET, Université du Québec à Montréal
CP 8888 Succursale Centre-ville
Montréal H3C 3P8
Lenhard Ng
Department of Mathematics
Duke University
Box 90320
Durham, NC 27708-0320
Steven Sivek
Department of Mathematics
Princeton University
Fine Hall, Washington Road
Princeton, NJ 08544-1000