Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unbounded $\mathfrak{sl}_3$-laminations and their shear coordinates   We study the space $\mathcal{L}_{\mathfrak{sl}_3}^x(\Sigma,\mathbb{Q})$ of
rational unbounded $\mathfrak{sl}_3$-laminations on a marked surface $\Sigma$.
We introduce an $\mathfrak{sl}_3$-analogue of the Thurston's shear coordinates
associated with any decorated triangulation, which gives rise to a natural
identification $\mathcal{L}_{\mathfrak{sl}_3}^x(\Sigma,\mathbb{Q}) \cong
\mathcal{X}_{\mathfrak{sl}_3,\Sigma}^\mathrm{uf}(\mathbb{Q}^{\mathrm{trop}})$.
We also introduce the space $\mathcal{L}^p(\Sigma,\mathbb{Q})$ of rational
unbounded $\mathfrak{sl}_3$-laminations with pinnings, which possesses the
frozen coordinates as well. Then we give a tropical anologue of the
amalgamation maps [FG06b] between them, which is indeed a procedure of gluing
$\mathfrak{sl}_3$-laminations with "shearings". We also investigate a relation
to the graphical basis of the $\mathfrak{sl}_3$-skein algebra [IY21], which
conjecturally leads to a quantum duality map.

11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga