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On complex line arrangements and their boundary manifolds


Let ${\mathcal A}$ be a line arrangement in the complex projective plane $\mathds{C}\mathds{P}^2$. We define and describe the inclusion map of the boundary manifold, the boundary of a closed regular neighbourhood of ${\mathcal A}$, in the exterior of the arrangement. We obtain two explicit descriptions of the map induced on the fundamental groups. These computations provide a new minimal presentation of the fundamental group of the complement.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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