A conjugation-free geometric presentation of fundamental groups of arrangements

Meital Eliyahu, David Garber, Mina Teicher

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)247-271
Number of pages25
JournalManuscripta Mathematica
Volume133
Issue number1
DOIs
StatePublished - 2010

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