Exact Lagrangian fillings of twist-spun torus links
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Abstract
We construct exact Lagrangian fillings of Legendrian torus links Λ(k,n−k) that are fixed by a Legendrian loop that acts by 2πℓ/n rotation. Using these rotationally symmetric fillings, we produce fillings of the corresponding Legendrian twist-spun tori. Our construction is combinatorial in nature, relating symmetric weakly separated collections and plabic graphs to symmetric Legendrian weaves via the T-shift procedure of Casals, Le, Sherman-Bennett, and Weng. The main technical ingredient in this process is a necessary and sufficient condition for the existence of maximal weakly separated collections of k-element subsets of {1,…,n} that are fixed by addition of ℓ modulo n.
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Scholars@Duke
James Michael Hughes
My research is in low-dimensional contact and symplectic topology. I primarily focus on invariants of Legendrian knots and their exact Lagrangian fillings, particularly those related to cluster theory. I also like to think about different constructions of Legendrian surfaces, especially from a cluster-theoretic perspective.
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