Torsion in linearized contact homology for Legendrian knots

Abstract

We present examples of Legendrian knots in ${\mathbb{R}}^3$ that have linearized Legendrian contact homology over $\mathbb{Z}$ containing torsion. As a consequence, we show that there exist augmentations of Legendrian knots over $\mathbb{Z}$ that are not induced by exact Lagrangian fillings, even though their mod $2$ reductions are.

19 pages, 7 figures. V2: minor revisions; accepted for publication in Michigan Math. J