Unbounded sl(3)-laminations and their shear coordinates

Abstract: Fock--Goncharov pointed out the space of unbounded laminations on a marked surface gives the set of tropical valued points of the moduli space of the framed PGL_2 local systems on the surface. The key point of this identification is that the shear coordinate of the space of unbounded laminations gives the tropicalized cluster structure of the moduli space. In this talk, we introduce the space of unbounded sl(3) laminations (with pinnings) and define the "shear coordinate" on it as a generalization of the sl(2) case. If time permits, we discuss the graphical basis of the Ishibashi--Yuasa sl(3) skein algebra. This talk is based on a joint work with Tsukasa Ishibashi.

mathematical physicsalgebraic geometrygeometric topologyquantum algebra

Audience: researchers in the discipline

Geometry, Algebra and Physics at KIAS