Open book decompositions of fiber sums in contact topology

Klukas, Mirko

doi:10.2140/agt.2016.16.1253

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Open book decompositions of fiber sums in contact topology

Mirko Klukas

Algebraic & Geometric Topology 16 (2016) 1253–1277

DOI: 10.2140/agt.2016.16.1253

Abstract

We describe compatible open books for the fiber connected sum along binding components and along multisections of open books. As an application, the first description provides simple ways of constructing open books supporting all tight contact structures on $T^{3}$ , recovering a result by Van Horn-Morris, as well as an open book supporting the result of a Lutz twist along a binding component of an open book, recovering a result by Ozbagci and Pamuk.

Keywords

open book decomposition, contact topology, fiber sums, binding sum, braided knots, transverse knots

Mathematical Subject Classification 2010

Primary: 57M50, 57MXX

References

Publication

Received: 17 July 2012

Revised: 14 August 2015

Accepted: 17 August 2015

Published: 1 July 2016

Authors

Mirko Klukas
Mathematisches Institut Universität zu Köln Weyertal 86–90 D-50931 Köln Germany

Volume 16, issue 3 (2016)