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 $n\ge 3$, $n\ne 4$, 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 $G$.

5 pages, accepted version

References in corpus (1)

• Lagrangian Cobordisms via Generating Families: Constructions and Geography