Real Algebraic and Analytic Geometry |

Real line arrangements and fundamental groups.

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homepage: http://fraise.univ-brest.fr/~huisman/

Submission: 2003, April 13.

*Abstract:
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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