Unbounded 𝔰𝔩3-laminations and their shearcoordinates

Generalizing the work of Fock and Goncharov on rational unbounded laminations, we give a geometric model of the tropical points of the cluster variety X sl 3 ; , which we call unbounded sl 3 -laminations, based on Kuperberg's sl 3 -webs.We introduce their tropical cluster coordinates as an sl 3 -analogue of Thurston's shear coordinates associated with any ideal triangulation.As a tropical analogue of gluing morphisms among the moduli spaces P PGL 3 ; of Goncharov and Shen, we describe a geometric gluing procedure of unbounded sl 3 -laminations with pinnings via "shearings".We also investigate a relation to the graphical basis of the sl 3 -skein algebra of Ishibashi and Yuasa (2023), which conjecturally leads to a quantum duality map.