2014/11/05 by Christopher R. Cornwell, Lenhard Ng, Steven Sivek · 2 citations
Mathematics · #math.SG #math.GT #msc:57M25 #msc:57R17 #msc:53D42 #msc:53D12
paper · pdf · doi:10.2140/agt.2016.16.797
published as Algebr. Geom. Topol. 16 (2016) 797-824 · 21 pages, 9 figures
arxiv created 2014/11/05 · arxiv updated 2016/05/04
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 non-reversible 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.