Obstructions to Lagrangian concordance

We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in $ℝ^{3}$ . 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.

PDF Access Denied

Warning: We have not been able to recognize your IP address 47.88.87.18 as that of a subscriber to this journal. Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form.

Or, visit our subscription page for instructions on purchasing a subscription. You may also contact us at contact@msp.org or by using our contact form.

Or, you may purchase this single article for USD 29.95:

Keywords

Legendrian knots, Lagrangian concordance

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 57R17, 53D42, 53D12

References

Publication

Received: 26 November 2014

Revised: 6 July 2015

Accepted: 15 July 2015

Published: 26 April 2016

Authors

Christopher Cornwell
CIRGET, Université du Québec à Montréal CP 8888 Succursale Centre-ville Montréal H3C 3P8 Canada
http://thales.math.uqam.ca/~cornwell/
Lenhard Ng
Department of Mathematics Duke University Box 90320 Durham, NC 27708-0320 USA
http://math.duke.edu/~ng/
Steven Sivek
Department of Mathematics Princeton University Fine Hall, Washington Road Princeton, NJ 08544-1000 USA
http://math.princeton.edu/~sivek

Volume 16, issue 2 (2016)

Christopher Cornwell, Lenhard Ng and Steven Sivek

Abstract