2023/12/10 by M. Firat Arikan, Arikan, M. Firat
Mathematics · #57R65 #58A05 #58D27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2312.05823
openalex publication_date 2023/12/10 · openalex created_date 2023/12/13 · openalex updated_date 2026/07/28
It is known that the folded sum of two contact mapping tori whose fibers are compact exact symplectic manifolds having a common convex boundary (called the ``fold'') admits a cooriented contact structure compatible with the obvious fibration map onto the circle. Here we first provide an alternative bundle-theoretical construction of such a ``folded'' contact structure based on a gluing process near the fold. Moreover, we prove that in any odd dimension 2n+1≥ 7 a folded contact structure on a folded sum of two contact mapping tori is tight if the induced contact form on the (common) contact fold admits no contractible Reeb orbit. In particular, any contact mapping torus of an odd dimension 2n+1≥ 7 is tight if the induced contact form on the convex boundary of a fiber admits no contractible Reeb orbit.