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January 2021 Nested Open Books And The Binding Sum
Sebastian Durst, Mirko Klukas
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Osaka J. Math. 58(1): 189-212 (January 2021).


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.


We thank an anonymous referee for bringing Mori's construction to our attention.


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Sebastian Durst. Mirko Klukas. "Nested Open Books And The Binding Sum." Osaka J. Math. 58 (1) 189 - 212, January 2021.


Received: 26 October 2017; Revised: 15 October 2019; Published: January 2021
First available in Project Euclid: 9 May 2021

Primary: 57R17
Secondary: 57R65

Rights: Copyright © 2021 Osaka University and Osaka City University, Departments of Mathematics

Vol.58 • No. 1 • January 2021
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