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Obstructions to
Lagrangian concordance
Christopher Cornwell, Lenhard Ng and Steven Sivek |
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Algebraic & Geometric Topology 16 (2016) 797–824
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Abstract |
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We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in . 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 crossings that have Legendrian representatives that are Lagrangian slice. |
Keywords
Legendrian knots, Lagrangian concordance
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Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57R17, 53D42, 53D12
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References |
Publication
Received: 26 November 2014
Revised: 6 July 2015
Accepted: 15 July 2015
Published: 26 April 2016
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Authors |
| Christopher Cornwell | |
| CIRGET, Université du Québec à
Montréal CP 8888 Succursale Centre-ville Montréal H3C 3P8 Canada |
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| http://thales.math.uqam.ca/~cornwell/ | |
| Lenhard Ng | |
| Department of Mathematics Duke University Box 90320 Durham, NC 27708-0320 USA |
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| http://math.duke.edu/~ng/ | |
| Steven Sivek | |
| Department of Mathematics Princeton University Fine Hall, Washington Road Princeton, NJ 08544-1000 USA |
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| http://math.princeton.edu/~sivek | |
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