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

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

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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Veröffentlicht in:arXiv.org 2012-01
Hauptverfasser: Bartolo, Enrique Artal, Cogolludo-Agustin, Jose I, Ortigas-Galindo, Jorge
Format: Artikel
Sprache:eng
Schlagworte:
Computation
Mathematics - Algebraic Geometry
Mathematics - Geometric Topology
Toruses
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Zusammenfassung: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1201.3274