English

On torsion in linearized Legendrian contact homology

Symplectic Geometry 2023-08-14 v2

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 GG and a positive integer n3n\geq 3, n4n\neq 4, we construct examples of Legendrian submanifolds of the standard contact vector space R2n+1\mathbb R^{2n+1}, whose n1n-1-th linearized Legendrian contact (co)homology over Z\mathbb Z computed with respect to a certain augmentation is isomorphic to GG.

Keywords

Cite

@article{arxiv.2210.09203,
  title  = {On torsion in linearized Legendrian contact homology},
  author = {Roman Golovko},
  journal= {arXiv preprint arXiv:2210.09203},
  year   = {2023}
}

Comments

5 pages, accepted version