2016/10/24 by Sebastian Durst, Durst, Sebastian, Mirko Klukas +1 · 1 citation
Mathematics · #57R17 (primary) #57R65 (secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1610.07356
openalex publication_date 2016/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of a nested open book, a submanifold equipped with an open book structure compatible with an ambient open book, and describe in detail the special case of a push-off of the binding of an open book. This enables us to explicitly describe a natural open book decomposition of a fibre connected sum of two open books along their bindings, provided they are diffeomorphic and admit an open book structure themselves. Furthermore, we apply the results to contact open books, showing that the natural open book structure of a contact fibre connected sum of two adapted open books along their contactomorphic bindings is again adapted to the resulting contact structure.