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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 (p,q)–torus curves.

Keywords
algebraic curve, fundamental group, braid monodromy
Mathematical Subject Classification 2010
Primary: 14F45, 14H30, 14H50
Secondary: 57M05, 57M12, 14H10, 14E05
References
Publication
Received: 16 January 2012
Revised: 23 March 2012
Accepted: 28 March 2012
Published: 9 June 2012
Authors
Enrique Artal Bartolo
Departamento de Matemáticas, IUMA
Universidad de Zaragoza
C/ Pedro Cerbuna 12
50009 Zaragoza
Spain
http://riemann.unizar.es/geotop/WebGeoTo/Profes/eartal/
José Ignacio Cogolludo Agustín
Departamento de Matemáticas, IUMA
Universidad de Zaragoza
C/ Pedro Cerbuna 12
50009 Zaragoza
Spain
http://riemann.unizar.es/~jicogo/
Jorge Ortigas-Galindo
Centro Universitario de la Defensa-IUMA
Universidad de Zaragoza
Academia General Militar
Ctra de Huesca s/n
50090 Zaragoza
Spain
http://riemann.unizar.es/~jortigas/