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arXiv · 2603.29352

Cylindrical contact homology for weakly convex contact forms in dimension three

Ana Kelly de Oliveira·Pedro A. S. Salomão
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Abstract

A contact form $λ$ on a closed contact three-manifold $(M,ξ)$ is called weakly convex if either it has no contractible Reeb orbit, or the first Chern class of $ξ$ vanishes on $π_2(M)$, and the index of every contractible Reeb orbit is at least $2$. We present conditions for a weakly convex contact form to admit a well-defined cylindrical contact homology. The key point is a cancellation mechanism for boundary degenerations involving index-2 Reeb orbits, based on a parity property of holomorphic planes.

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Ana Kelly de Oliveira, Pedro A. S. Salomão. 2026-03-31. Cylindrical contact homology for weakly convex contact forms in dimension three. https://arxiv.org/abs/2603.29352

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