Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weave Realizability for D-type   We study exact Lagrangian fillings of Legendrian links of $D_n$-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
$D_n$-type have at least as many Hamiltonian isotopy classes of Lagrangian
fillings as cluster seeds in the $D_n$-type cluster algebra, and their
geometric exchange graph for Lagrangian disk surgeries contains the cluster
exchange graph of $D_n$-type.

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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn