Volume 12, issue 3 (2012)

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

Enrique Artal Bartolo, José Ignacio Cogolludo Agustín and Jorge Ortigas-Galindo

Algebraic & Geometric Topology 12 (2012) 1265–1272
Abstract

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 $\left(p,q\right)$–torus curves.

Keywords
algebraic curve, fundamental group, braid monodromy
Mathematical Subject Classification 2010
Primary: 14F45, 14H30, 14H50
Secondary: 57M05, 57M12, 14H10, 14E05