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Legendrian loops and cluster modular groups
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abstract
This work studies Legendrian loop actions on exact Lagrangian fillings of Legendrian links in $(\R^3, \xi_{\st})$. By identifying the induced action of Legendrian loops as generators of cluster modular groups, we establish the existence of faithful group actions on the exact Lagrangian fillings of several families of Legendrian positive braid closures, including all positive torus links. In addition, we leverage a Nielsen-Thurston-like classification of cluster automorphisms to provide new combinatorial and algebraic tools for proving that a Legendrian loop action has infinite order.
Forward citations
Cited by 2 Pith papers
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Legendrian doubles, twist spuns, and clusters
The authors construct cluster structures on sheaf moduli of twist-spun Legendrian surfaces and use them to produce new exact Lagrangian fillings and obstructions in contact R^5.
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Cluster automorphism group of braid varieties
An explicit inverse matrix A_{u,beta} is constructed for braid varieties; its frozen columns generate the cluster automorphism group action, and the matrix is proven invertible with determinant plus or minus one.
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