ON RIGHT-ANGLED ARTIN GROUPS WHOSE UNDERLYING GRAPHS HAVE TWO VERTICES WITH THE SAME LINK

Title & Authors
ON RIGHT-ANGLED ARTIN GROUPS WHOSE UNDERLYING GRAPHS HAVE TWO VERTICES WITH THE SAME LINK
Kim, Jongtae; Moon, Myoungho;

Abstract
Let $\small{{\Gamma}}$ be a graph which contains two vertices $\small{a}$, $\small{b}$ 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($\small{{\Gamma}}$) contains a hyperbolic surface subgroup, then A($\small{{\Gamma}}$-{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.
Keywords
right-angled Artin group;hyperbolic surface subgroup;
Language
English
Cited by
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