TY - JOUR
T1 - A conjugation-free geometric presentation of fundamental groups of arrangements
AU - Eliyahu, Meital
AU - Garber, David
AU - Teicher, Mina
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77954886494&partnerID=8YFLogxK
U2 - 10.1007/s00229-010-0380-2
DO - 10.1007/s00229-010-0380-2
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AN - SCOPUS:77954886494
SN - 0025-2611
VL - 133
SP - 247
EP - 271
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 1
ER -