Classical cylindrical contact homology is not invariant over $\bZ$

Soham Chanda

Home/Archive/arXiv

arXiv · 2610.11189

Classical cylindrical contact homology is not invariant over $\bZ$

Soham Chanda

View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that classical cylindrical contact homology over $\mathbb{Z}$, equipped with its decomposition by free homotopy classes, is not invariant under changes of hypertight contact form. Specifically, we construct two nondegenerate hypertight perturbations of the standard Seifert contact form on $Σ(2,4,5)$ whose cylindrical contact homologies in the regular-fiber class are respectively torsion-free and contain $\mathbb{Z}/5$-torsion.

Explore related subjects

math.SG

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Soham Chanda. 2026-10-08. Classical cylindrical contact homology is not invariant over $\bZ$. https://arxiv.org/abs/2610.11189

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bi-contact plugs and dynamical hyperbolicity

We develop a theory of bi-contact plugs in dimension three to construct Anosov flows or, more generally, structurally stable nonsingular flows. For a transversely orientable hyperbolic plug with orientable filling Morse-Smale boundary laminations, we prove that every strongly transverse gluing map can be isotoped through strongly transverse maps to identify a strongly adapted contact form up to sign. The resulting flow is hyperbolic and is Anosov when the quotient is closed. This answers a question of Béguin-Bonatti-Yu under the stated orientability assumptions. The result also extends to gluing nonsingular partially hyperbolic flows. Anosov completion by reflection embeds each such hyperbolic plug in an Anosov flow on its oriented double. Further applications include a classification of structurally generic transversely oriented projectively Anosov flows without saddle periodic orbits, Morse-Smale examples with prescribed saddle count, a generalization of the construction of Bonatti-Bowden-Potrie to give embeddings of (attracting) hyperbolic plugs into (partially hyperbolic) projectively Anosov flows with the same topological entropy, and constructions on doubles and torus bundles with controlled invariant torus dynamics. Finally, every cooriented partially hyperbolic bi-contact plug admits a Liouville structure on its thickening, with Liouville trajectories projecting to positively reparametrized flow lines. Repelling plugs yield four-dimensional Liouville domains, often with chaotic skeletons.

math.SG↗

arXiv2026

Perverse Microsheaves

On a complex contact manifold, or complex symplectic manifold with weight-1 circle action, we construct a sheaf of stable categories carrying a t-structure which is locally equivalent to a microlocalization of the perverse t-structure.

math.SG↗

arXiv2026

Fillability obstructions for high-dimensional confoliations

In this paper, we study confoliations in dimensions higher than three, mostly from the perspective of symplectic fillability. Our main result is that Massot-Niederkrüger-Wendl's bordered Legendrian open book, an object that obstructs the weak symplectic fillability of contact manifolds, admits a generalization for confoliations equipped with symplectic data. Applications include the non-fillability of the product of an overtwisted contact manifold and a class of symplectic manifolds, and the fact that Bourgeois contact structures associated with overtwisted contact manifolds admit no weak symplectic fillings for which the symplectic structure restricts at the boundary to a positive generator of the second cohomology of the torus factor. In addition, along the lines of the original 3-dimensional work of Eliashberg and Thurston, we give a new definition of approximation and deformation of confoliations by contact structures and describe some natural examples.

math.SG↗