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math.GT2026
Hard Legendrian unknots
Joseph Breen, Austin Christian, Angela Wu
We initiate the study of Reidemeister hardness of Legendrian unknot front projections. Using normal rulings, we obstruct several infinite families of hard unknot diagrams from bein…
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.GT2020★ 2 cited
Some applications of Menke's JSJ decomposition for symplectic fillings
Austin Christian, Youlin Li
We apply Menke's JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserv…