We study $g$-vector cones in a cluster algebra defined from a weighted orbifold of rank $n$ introduced by Felikson, Shapiro and Tumarkin. We determine the closure of the union of the $g$-vector cones. It is equal to $\mathbb{ R}^n$ except for a weighted orbifold with empty boundary and exactly one puncture, in which case it is equal to the half space of a certain explicit hyperplane in $\mathbb{ R}^n$.
Categories: math.CO math.GT math.RA math.RT
