Cluster Varieties from Legendrian Knots


We show that many interesting spaces — including all positroid strata and wild character varieties — are moduli of constructible sheaves on a surface with microsupport in a Legendrian link. We recover the cluster structures on these spaces from the Floer theory of Lagrangian fillings of these Legendrians. We also use results in cluster algebra to construct and distinguish exact Lagrangian fillings of Legendrian links in the standard contact three space.

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@inproceedings{Shende2016ClusterVF, title={Cluster Varieties from Legendrian Knots}, author={Vivek V. Shende and DAVID TREUMANN and Harold Williams and Eric Zaslow}, year={2016} }