On Right-Angled Artin Groups Whose Underlying Graphs Have Two Vertices With the Same Link

Abstract

Abstract. Let Γ be a graph which contains two vertices a, b with the same link. For the case where the link has less than 3 vertices, we prove that if the right-angled Artin group A(Γ) contains a hyperbolic surface subgroup, then A(Γ−{a}) contains a hyperbolic surface subgroup. Moreover, we also show that the same result holds with certain restrictions for the case where the link has more than or equal to 3 vertices.