2026/03/31 by Ana Kelly de Oliveira, Pedro A. S. Salomão · 1 voice
Mathematics · #math.SG
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 π2(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.