Artin presentations and fundamental groups of 3-manifolds

Abstract

We prove that the set of n-Artin presentations has a group structure. It is a known result but it seems that it does not appear explicitly in the literature. As an application we consider a special class of integral framed links β ˆ in S 3 such that β = ∏ i = 1 n Δ 2 e σ 1 2 e i σ 2 2 f i and we calculate the fundamental group of the 3-manifolds obtained by integral Dehn surgery on these links. In some cases we say when the groups obtained cannot be trivial.