2008/09/29 by Vincent Colin, Colin, Vincent, Ko Honda +1 · 2 citations
Mathematics · #53C15 #57M50 #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT #msc:53C15 #msc:57M50
paper · pdf · doi:10.48550/arxiv.0809.5088
58 pages, 10 figures
arxiv created 2008/09/29 · openalex publication_date 2008/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We determine parts of the contact homology of certain contact 3-manifolds in the framework of open book decompositions, due to Giroux. We study two cases: when the monodromy map of the compatible open book is periodic and when it is pseudo-Anosov. For an open book with periodic monodromy, we verify the Weinstein conjecture. In the case of an open book with pseudo-Anosov monodromy, suppose the boundary of a page of the open book is connected and the fractional Dehn twist coefficient c=k\over n, where n is the number of prongs along the boundary. If k≥ 2, then there is a well-defined linearized contact homology group. If k≥ 3, then the linearized contact homology is exponentially growing with respect to the action, and every Reeb vector field of the corresponding contact structure admits an infinite number of simple periodic orbits.