Computation-free presentation of the fundamental group of generic $(p,q)$-torus curves (1201.3274v1)

Abstract: In this note, we present a new method for computing fundamental groups of curve complements using a variation of the Zariski-Van Kampen method on general ruled surfaces. As an application we give an alternative (computation-free) proof for the fundamental group of generic $(p,q)$-torus curves.