Contact 3-manifolds admitting uniform spinal open books with planar pages have their weak, strong, and exact symplectic and Stein fillings classified by diffeomorphism classes of Lefschetz fibrations.
Lectures on Holomorphic Curves in Symplectic and Contact Geometry
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abstract
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from readers, I've decided to make a presentable half-finished version available here. Further chapters will be added in future updates.
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2020 1verdicts
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On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification
Contact 3-manifolds admitting uniform spinal open books with planar pages have their weak, strong, and exact symplectic and Stein fillings classified by diffeomorphism classes of Lefschetz fibrations.