Geodesic
Computation-free presentation of the fundamental group of generic (p,q)–torus curves
Artal Bartolo, Enrique1 ; Cogolludo Agustín, José Ignacio1 ; Ortigas-Galindo, Jorge2
1Departamento de Matemáticas, IUMA, Universidad de Zaragoza, C/ Pedro Cerbuna 12, 50009 Zaragoza, Spain
2Centro Universitario de la Defensa-IUMA, Universidad de Zaragoza, Academia General Militar, Ctra de Huesca s/n, 50090 Zaragoza, Spain
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1265-1272
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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.

DOI : 10.2140/agt.2012.12.1265
Classification : 14F45, 14H30, 14H50, 57M05, 57M12, 14H10, 14E05
Keywords: algebraic curve, fundamental group, braid monodromy

Artal Bartolo, Enrique  1   ; Cogolludo Agustín, José Ignacio  1   ; Ortigas-Galindo, Jorge  2

1 Departamento de Matemáticas, IUMA, Universidad de Zaragoza, C/ Pedro Cerbuna 12, 50009 Zaragoza, Spain
2 Centro Universitario de la Defensa-IUMA, Universidad de Zaragoza, Academia General Militar, Ctra de Huesca s/n, 50090 Zaragoza, Spain 
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Artal Bartolo, Enrique; Cogolludo Agustín, José Ignacio; Ortigas-Galindo, Jorge. Computation-free presentation of the fundamental group of generic (p,q)–torus curves. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1265-1272. doi: 10.2140/agt.2012.12.1265

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