Volume 10, issue 3 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21, 1 issue

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
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
Bibliography
1 W A Arvola, The fundamental group of the complement of an arrangement of complex hyperplanes, Topology 31 (1992) 757 MR1191377
2 A D R Choudary, A Dimca, Ş Papadima, Some analogs of Zariski’s theorem on nodal line arrangements, Algebr. Geom. Topol. 5 (2005) 691 MR2153112
3 D C Cohen, A I Suciu, The braid monodromy of plane algebraic curves and hyperplane arrangements, Comment. Math. Helv. 72 (1997) 285 MR1470093
4 M Falk, Homotopy types of line arrangements, Invent. Math. 111 (1993) 139 MR1193601
5 K M Fan, On parallel lines and free groups arXiv:0905.1178
6 K M Fan, Position of singularities and the fundamental group of the complement of a union of lines, Proc. Amer. Math. Soc. 124 (1996) 3299 MR1343691
7 K M Fan, Direct product of free groups as the fundamental group of the complement of a union of lines, Michigan Math. J. 44 (1997) 283 MR1460414
8 D Garber, On the fundamental groups of complements of plane curves, PhD thesis, Bar-Ilan University (2001)
9 D Garber, M Teicher, U Vishne, π1–classification of real arrangements with up to eight lines, Topology 42 (2003) 265 MR1928653
10 M Hall Jr., The theory of groups, Chelsea Publishing Co. (1976) MR0414669
11 T Jiang, S S T Yau, Diffeomorphic types of the complements of arrangements of hyperplanes, Compositio Math. 92 (1994) 133 MR1283226
12 D L Johnson, Presentations of groups, 22, Cambridge Univ. Press (1976) MR0396763
13 E R V Kampen, On the fundamental group of an algebraic curve, Amer. J. Math. 55 (1933) 255 MR1506962
14 R C Lyndon, P E Schupp, Combinatorial group theory, 89, Springer (1977) MR0577064
15 W Magnus, A Karrass, D Solitar, Combinatorial group theory.Presentations of groups in terms of generators and relations, Dover (1976) MR0422434
16 B Moishezon, M Teicher, Braid group technique in complex geometry. I. Line arrangements in CP2, from: "Braids (Santa Cruz, CA, 1986)" (editors J S Birman, A Libgober), Contemp. Math. 78, Amer. Math. Soc. (1988) 425 MR975093
17 M Oka, K Sakamoto, Product theorem of the fundamental group of a reducible curve, J. Math. Soc. Japan 30 (1978) 599 MR513072
18 P Orlik, H Terao, Arrangements of hyperplanes, 300, Springer (1992) MR1217488
19 R Randell, The fundamental group of the complement of a union of complex hyperplanes, Invent. Math. 69 (1982) 103 MR671654
20 S Wang, S S T Yau, Rigidity of differentiable structure for new class of line arrangements, Comm. Anal. Geom. 13 (2005) 1057 MR2216152