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arXiv · 1810.12017

On symplectic fillings of spinal open book decompositions I: Geometric constructions

Samuel Lisi·Jeremy Van Horn-Morris·Chris Wendl
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Abstract

A spinal open book decomposition on a contact manifold is a generalization of a supporting open book which exists naturally e.g. on the boundary of a symplectic filling with a Lefschetz fibration over any compact oriented surface with boundary. In this first paper of a two-part series, we introduce the basic notions relating spinal open books to contact structures and symplectic or Stein structures on Lefschetz fibrations, leading to the definition of a new symplectic cobordism construction called spine removal surgery, which generalizes previous constructions due to Eliashberg, Gay-Stipsicz and the third author. As an application, spine removal yields a large class of new examples of contact manifolds that are not strongly (and sometimes not weakly) symplectically fillable. This paper also lays the geometric groundwork for a theorem to be proved in part II, where holomorphic curves are used to classify the symplectic and Stein fillings of contact 3-manifolds admitting a spinal open book with a planar page.

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Samuel Lisi, Jeremy Van Horn-Morris, Chris Wendl. 2018-10-29. On symplectic fillings of spinal open book decompositions I: Geometric constructions. https://arxiv.org/abs/1810.12017

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