Mixed tori in contact surgery diagrams
Austin Christian, Tanushree Shah

TL;DR
This paper introduces a diagrammatic method for applying the symplectic JSJ decomposition to classify exact and weak symplectic fillings of 3-dimensional contact manifolds, including lens spaces and plumbed manifolds.
Contribution
It develops a new diagrammatic framework for symplectic JSJ decomposition and provides an algorithm for classifying symplectic fillings of various 3-manifolds.
Findings
Recovered known classifications for lens spaces and torus bundles.
Provided an algorithm for classifying fillings of plumbed 3-manifolds.
Established a diagrammatic approach to symplectic JSJ decomposition.
Abstract
We develop a diagrammatic framework for applying the symplectic JSJ decomposition to exact/weak symplectic fillings of 3-dimensional contact manifolds. Namely, we apply the symplectic JSJ decomposition to a contact surgery diagram for some , producing a finite collection of contact manifolds, also described diagrammatically, whose exact/weak symplectic fillings determine those of . We apply this technique to recover known symplectic filling classifications for certain lens spaces and torus bundles, and also to provide an algorithm for classifying the exact/weak symplectic fillings of a large class of plumbed 3-manifolds.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics
