Real Algebraic and Analytic Geometry
Submission: 2003, April 13.
Let A be a real line arrangement in the real projective plane, and let A' be its complexification. Let C' be the complement of the line arrangement A' in the complex projective plane. The Galois group G of C/R acts on C'. We construct a G-equivariant strong deformation retract of C'. As an application, we give a presentation of the orbifold fundamental group of C'//G, and deduce a presentation of the ordinary fundamental group of C'.
Mathematics Subject Classification (2000): 14P25, 52C30, 57M05.
Keywords and Phrases: real line arrangement, strong deformation retract, fundamental group, orbifold fundamental group, equivariant fundamental group, presentation.
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