Cluster varieties from Legendrian knots
By Vivek V. Shende, David Treumann, Harold Williams, Eric Zaslow. Duke mathematical journal, 2015
101 citations recorded by the source corpus.
Author(s): Shende, V; Treumann, D; Williams, H; Zaslow, E | Abstract: © 2019 Duke University Press. All rights reserved. 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 show that the existence of cluster structures on these spaces may be deduced in a uniform, systematic fashion by constructing and taking the sheaf quantizations of a set of exact Lagrangian fillings in correspondence with isotopy representatives whose front projections have crossings with alternating orientations. It follows in turn that results in cluster algebra may be used to construct and distinguish exact Lagrangian fillings of Legendrian links in the standard contact three space.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/37179203d72e955c1950a273895b2661a750a6ef
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Citations in the corpus
- BPS spectra and 3-manifold invariants (2017, background): “ots). The unreduced version, on the other hand, categories unnormalized HOMFLY-PT polynomial and is innite-dimensional for any color . The former has no obvious analogue for 3-manifolds. { 25 { In [61], the moduli space M(L K) is described as a cluster variety. Another simple example is K= unknot an”
- Infinitely many Lagrangian fillings (2020, background): “SinceM(Λ(n,m)) is a Legendrian isotopy invariant [39, 64, 65], it defines a monodromy representation Γ : π1(L(n,m)) −→ Aut(M(Λ(n,m))), into the space of algebraic automorphisms of the algebraic variety M(Λ(n,m)).”