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

Enrique Artal Bartolo; Jorge Ortigas-Galindo; Jose I. Cogolludo-Agustin

arxiv: 1201.3274 · v1 · pith:X646J45Gnew · submitted 2012-01-16 · 🧮 math.AG · math.GT

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

Enrique Artal Bartolo , Jose I. Cogolludo-Agustin , Jorge Ortigas-Galindo This is my paper

classification 🧮 math.AG math.GT

keywords fundamentalcomputation-freecurvesgenericgroupmethodtorusalternative

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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.

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

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