|
|||||
|
|
|
|
|
|
|
|
|
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/ | |
|
