Volume 10, issue 3 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The characterization of a line arrangement whose fundamental group of the complement is a direct sum of free groups

Meital Eliyahu, Eran Liberman, Malka Schaps and Mina Teicher

Algebraic & Geometric Topology 10 (2010) 1285–1304
Abstract

Kwai Man Fan proved that if the intersection lattice of a line arrangement does not contain a cycle, then the fundamental group of its complement is a direct sum of infinite and cyclic free groups. He also conjectured that the converse is true as well. The main purpose of this paper is to prove this conjecture.

Keywords
fundamental group, line arrangement, direct sum of free groups, hyperplane arrangement, graph of line arrangement
Mathematical Subject Classification 2000
Primary: 14F35, 32S22
Secondary: 14N30, 52C30
References
Publication
Received: 26 February 2009
Revised: 14 October 2009
Accepted: 10 November 2009
Published: 4 June 2010
Authors
Meital Eliyahu
Department of Mathematics
Bar Ilan University
52900 Ramat Gan
Israel
Eran Liberman
Department of Mathematics
Bar Ilan University
52900 Ramat Gan
Israel
Malka Schaps
Department of Mathematics
Bar Ilan University
52900 Ramat Gan
Israel
Mina Teicher
Department of Mathematics
Bar Ilan University
52900 Ramat Gan
Israel
http://www.cs.biu.ac.il/~teicher/