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 [Formula: see text] and a positive integer [Formula: see text], [Formula: see text], we construct examples of Legendrian submanifolds of the standard contact vector space [Formula: see text], whose [Formula: see text]th linearized Legendrian contact (co)homology over [Formula: see text] computed with respect to a certain augmentation is isomorphic to [Formula: see text].