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

2002/08/14 by David Garber, Mina Teicher
Mathematics · #math.GT #math.AT

paper · pdf

published as Complex Analysis and Algebraic Geometry, Edited by T. Peternell and F.-O. Schreyer, de Gruyter, 173-223 (2000) · 47 pages, 39 figures

arxiv created 2002/08/14 · arxiv updated 2009/11/30

Abstract

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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