The fundamental group's structure of the complement of some configurations of real line arrangements

Details The fundamental group's structure of the complement of some configurations of real line arrangements The fundamental group's structure of the complement of some configurations of real line arrangements

2002-08-14

arxiv.org/abs/math/0208113v1

Complex Analysis and Algebraic Geometry, Edited by T. Peternell and F.-O. Schreyer, de Gruyter, 173-223 (2000)

Mathematics

Geometric Topology

47 pages, 39 figures

Scientific paper

In this paper, we give a fully detailed exposition of computing fundamental groups of complements of line arrangements using the Moishezon-Teicher technique for computing the braid monodromy of a curve and the Van-Kampen theorem which induces a presentation of the fundamental group of the complement from the braid monodromy of the curve. For example, we treated the cases where the arrangement has t multiple intersection points and the rest are simple intersection points. In this case, the fundamental group of the complement is a direct sum of infinite cyclic groups and t free groups. Hence, the fundamental groups in these cases is ``big''. These calculations will be useful in computing the fundamental group of Hirzebruch covering surfaces.

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