Vol. 288, No. 2, 2017

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ISSN: 0030-8730
Augmentations and rulings of Legendrian links in $\#^k(S^1\times S^2)$

Caitlin Leverson

Vol. 288 (2017), No. 2, 381–423

Given a Legendrian link in #k(S1 × S2), we extend the definition of a normal ruling from J1(S1) given by Lavrov and Rutherford and show that the existence of an augmentation to any field of the Chekanov–Eliashberg differential graded algebra over [t,t1] is equivalent to the existence of a normal ruling of the front diagram. For Legendrian knots, we also show that any even graded augmentation must send t to 1. We use the correspondence to give nonvanishing results for the symplectic homology of certain Weinstein 4-manifolds. We show a similar correspondence for the related case of Legendrian links in J1(S1), the solid torus.

Legendrian knot, Legendrian submanifold, contact manifold, normal ruling
Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 53D42, 57M27
Received: 10 November 2015
Revised: 2 September 2016
Accepted: 30 October 2016
Published: 28 April 2017
Caitlin Leverson
School of Mathematics
Georgia Institute of Technology
School of Mathematics
686 Cherry Street
Atlanta, GA 30332
United States