2004/07/31 by Tamas Kalman · 1 citation
Mathematics · #math.GT #math.SG #msc:53D40 #msc:57M25
paper · pdf · doi:10.2140/gt.2005.9.2013
published as Geom. Topol. 9 (2005) 2013-2078 · Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper46.abs.html
arxiv created 2005/11/06 · arxiv updated 2014/11/11
We consider S1-families of Legendrian knots in the standard contact R3. We define the monodromy of such a loop, which is an automorphism of the Chekanov-Eliashberg contact homology of the starting (and ending) point. We prove this monodromy is a homotopy invariant of the loop. We also establish techniques to address the issue of Reidemeister moves of Lagrangian projections of Legendrian links. As an application, we exhibit a loop of right-handed Legendrian torus knots which is non-contractible in the space Leg(S1,R3) of Legendrian knots, although it is contractible in the space Emb(S1,R3) of smooth knots. For this result, we also compute the contact homology of what we call the Legendrian closure of a positive braid and construct an augmentation for each such link diagram.