2025/09/29 by Ishibashi, Tsukasa, Sun, Zhe, Yuasa, Wataru
#Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2509.25014
We introduce rational bounded \mathfraksp4-laminations on a marked surface \boldsymbolΣ as a proposed topological model for the rational tropical points ASp4,\boldsymbolΣ(ℚT) of the Fock--Goncharov moduli space [FG06]. Our space consists of certain equivalence classes of \mathfraksp4-webs introduced by Kuperberg [Kup96], together with rational measures. We define tropical coordinate systems using the \mathfraksp4-case of the intersection number of Shen--Sun--Weng [SSW25], and establish a bijection using the framework of the graded \mathfraksp4-skein algebra. This provides a topological perspective for Fock--Goncharov duality for \mathfraksp4.