Geodesic
Weave-realizability for D–type
Hughes, James1
1 Department of Mathematics, University of California, Davis, Davis, CA, United States
Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2735-2776

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We study exact Lagrangian fillings of Legendrian links of Dn–type in the standard contact 3–sphere. The main result is the existence of a Lagrangian filling, represented by a weave, such that any algebraic quiver mutation of the associated intersection quiver can be realized as a geometric weave mutation. The method of proof is via Legendrian weave calculus and a construction of appropriate 1–cycles whose geometric intersections realize the required algebraic intersection numbers. In particular, we show that, in D–type, each cluster chart of the moduli of microlocal rank-1 sheaves is induced by at least one embedded exact Lagrangian filling. Hence, the Legendrian links of Dn–type have at least as many Hamiltonian isotopy classes of Lagrangian fillings as cluster seeds in the Dn–type cluster algebra, and their geometric exchange graph for Lagrangian disk surgeries contains the cluster exchange graph of Dn–type.

DOI : 10.2140/agt.2023.23.2735
Keywords: Legendrian knots, exact Lagrangian fillings

Hughes, James 1

1 Department of Mathematics, University of California, Davis, Davis, CA, United States 
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Hughes, James. Weave-realizability for D–type. Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2735-2776. doi: 10.2140/agt.2023.23.2735

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