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arXiv · 2210.09203

On torsion in linearized Legendrian contact homology

Roman Golovko
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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 $G$.

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Roman Golovko. 2022-10-17. On torsion in linearized Legendrian contact homology. https://doi.org/10.1142/s0218216523500566

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