On torsion in linearized Legendrian contact homology

Abstrakt

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 = 3, n ?4, we construct examples of Legendrian submanifolds of the standard contact vector space R2n+1, whose n-1th linearized Legendrian contact (co)homology over Z computed with respect to a certain augmentation is isomorphic to G.

Klíčová slova

• Torsion
• linearized Legendrian contact homology
• augmentation
• exact Lagrangian filling