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

  • Received : 2011.11.25
  • Published : 2013.03.31

Abstract

Let ${\Gamma}$ 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(${\Gamma}$) contains a hyperbolic surface subgroup, then A(${\Gamma}$-{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

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