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arXiv · 2603.06031

Algebraic planar torsion in contact manifolds

Zhengyi Zhou
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Abstract

We demonstrate that the functorial properties of the symplectic field theory under strong cobordisms and surgery cobordisms can produce finite algebraic (planar) torsions from simple examples, which gives a unified treatment of most of the known computations of algebraic (planar) torsions. In addition, we obtain many families of new examples, notably including (1) stably fillable examples in all dimensions $\ge 5$ with algebraic (planar) torsion precisely $k$ for any given $k\in \mathbb{N}_+$, confirming a conjecture of Latschev and Wendl; (2) contact structures on spheres of all dimensions at least $5$ with finite algebraic planar torsion at least $1$, which implies that tight not weakly fillable contact structures are ubiquitous in higher dimensions. We also explain that all known examples of contact manifolds without strong/weak fillings in dimension $\ge 5$ have algebraic planar torsion.

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Zhengyi Zhou. 2026-03-06. Algebraic planar torsion in contact manifolds. https://arxiv.org/abs/2603.06031

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