Volume 11, issue 3 (2007)

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

Volume 26
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Combinatorial Morse theory and minimality of hyperplane arrangements

Mario Salvetti and Simona Settepanella

Geometry & Topology 11 (2007) 1733–1766
Bibliography
1 A Björner, G M Ziegler, Combinatorial stratification of complex arrangements, J. Amer. Math. Soc. 5 (1992) 105 MR1119198
2 N Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles 1337, Hermann (1968) MR0240238
3 D C Cohen, Cohomology and intersection cohomology of complex hyperplane arrangements, Adv. Math. 97 (1993) 231 MR1201844
4 D C Cohen, P Orlik, Arrangements and local systems, Math. Res. Lett. 7 (2000) 299 MR1764324
5 A Dimca, S Papadima, Hypersurface complements, Milnor fibers and higher homotopy groups of arrangments, Ann. of Math. $(2)$ 158 (2003) 473 MR2018927
6 H Esnault, V Schechtman, E Viehweg, Cohomology of local systems on the complement of hyperplanes, Invent. Math. 109 (1992) 557 MR1176205
7 R Forman, Morse theory for cell complexes, Adv. Math. 134 (1998) 90 MR1612391
8 R Forman, A user's guide to discrete Morse theory, Sém. Lothar. Combin. 48 (2002) MR1939695
9 D B Fuks, Cohomology of the braid group $\mathrm{mod} 2$, Funkcional. Anal. i Priložen. 4 (1970) 62 MR0274463
10 I M Gelfand, G L Rybnikov, Algebraic and topological invariants of oriented matroids, Dokl. Akad. Nauk SSSR 307 (1989) 791 MR1020668
11 T Kohno, Homology of a local system on the complement of hyperplanes, Proc. Japan Acad. Ser. A Math. Sci. 62 (1986) 144 MR846350
12 A Libgober, S Yuzvinsky, Cohomology of the Orlik–Solomon algebras and local systems, Compositio Math. 121 (2000) 337 MR1761630
13 P Orlik, H Terao, Arrangements of hyperplanes, Grundlehren der Mathematischen Wissenschaften 300, Springer (1992) MR1217488
14 R Randell, Morse theory, Milnor fibers and minimality of hyperplane arrangements, Proc. Amer. Math. Soc. 130 (2002) 2737 MR1900880
15 M Salvetti, Topology of the complement of real hyperplanes in $\mathbb{C}^N$, Invent. Math. 88 (1987) 603 MR884802
16 M Salvetti, The homotopy type of Artin groups, Math. Res. Lett. 1 (1994) 565 MR1295551
17 V Schechtman, H Terao, A Varchenko, Local systems over complements of hyperplanes and the Kac–Kazhdan conditions for singular vectors, J. Pure Appl. Algebra 100 (1995) 93 MR1344845
18 A I Suciu, Translated tori in the characteristic varieties of complex hyperplane arrangements, Topology Appl. 118 (2002) 209 MR1877726
19 M Yoshinaga, Hyperplane arrangements and Lefschetz's hyperplane section theorem, to appear in Kodai Math. J. (2007)
20 T Zaslavsky, Facing up to arrangements: face-count formulas for partitions of space by hyperplanes, Mem. Amer. Math. Soc. 1 (1975) MR0357135