3 papers
math.GT2025
Mixed tori in contact surgery diagrams
Austin Christian, Tanushree Shah
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 symplec…
math.SG2019
On symplectic fillings of virtually overtwisted torus bundles
Austin Christian
We use Menke's JSJ-type decomposition theorem for symplectic fillings to reduce the classification of strong and exact symplectic fillings of virtually overtwisted torus bundles to…
math.SG2019
Splitting symplectic fillings
Austin Christian, Michael Menke
We generalize the mixed tori which appear in the second author's JSJ-type decomposition theorem for symplectic fillings of contact manifolds. Mixed tori are convex surfaces in cont…