On Torsion in Linearized Legendrian Contact Homology

Abstract

In this short note we discuss certain examples of Legendrian submanifolds, whose linearized Legendrian contact (co)homology groups over integers have non-vanishing algebraic torsion. More precisely, for a given arbitrary finitely generated abelian group $G$ and a positive integer $n\geq 3$, $n\neq 4$, we construct examples of Legendrian submanifolds of the standard contact vector space $\mathbb R^{2n+1}$, whose $n-1$-th linearized Legendrian contact (co)homology over $\mathbb Z$ computed with respect to a certain augmentation is isomorphic to $G$.