A conjugation-free geometric presentation of fundamental groups of arrangements

作者：Eliyahu Meital; Garber David^*; Teicher Mina

来源：Manuscripta Mathematica, 2010, 133(1-2): 247-271.

DOI：10.1007/s00229-010-0380-2

We introduce the notion of a conjugation-free geometric presentation for a fundamental group of a line arrangement's complement, and we show that the fundamental groups of the following family of arrangements have a conjugation-free geometric presentation: A real arrangement L, whose graph of multiple points is a union of disjoint cycles, has no line with more than two multiple points, and where the multiplicities of the multiple points are arbitrary. We also compute the exact group structure ( by means of a semi-direct product of groups) of the arrangement of 6 lines whose graph consists of a cycle of length 3, and all the multiple points have multiplicity 3.

• 出版日期2010-9