Diffeomorphic types of the complements of arrangements of hyperplanes

 Access to full text

 Full (PDF)

1. [Arn] V.I. Arnold: The cohomology ring of the colored braid group. Mat. Sametki5 (1969) 227-231; Math. Notes5 (1969) 138-140. Zbl0277.55002MR242196
2. [Arv1] W. Arvola: The fundamental group of the complement of an arrangement of complex hyperplanes (preprint). Zbl0772.57001MR1191377
3. [Arv2] W. Arvola: Complexified real arrangements of hyperplanes (preprint). Zbl0731.57011MR1103735
4. [Bj-Zi] A. Björner and G. Ziegler: Combinatorial stratification of complex arrangements. J. Amer. Math. Soc., 1992. Zbl0754.52003MR1119198
5. [Br] E. Brieskorn: Sur les groups de tresses, in " Séminaire Bourbaki1971/72", Lecture Notes in Math. 317. Springer-Verlag: Berlin, Heidelberg, New York (1973) 21-44. Zbl0277.55003MR422674
6. [Ca] P. Cartier: Les arrangements d'hyperplans: un chapitre de géometrie combinatoire, in "Séminaire Bourbaki1980/81," Lecture Notes in Math. 901. Springer-Verlag, Berlin, Heidelberg, New York (1981) 1-22. Zbl0483.51011MR647485
7. [Co] H.S.M. Coxeter: Discrete groups generated by reflections. Annals of Math.35 (1934) 588-621. Zbl0010.01101MR1503182JFM60.0898.02
8. [De] P. Deligne: Les immeubles des groups de tresses génèralisés. Invent. Math.17 (1972) 273-302. Zbl0238.20034MR422673
9. [De-Mo] P. Deligne and G.D. Mostow: Monodromy of hypergeometric functions and non-lattice integral monodromy. Publ. Math. IHES63 (1986) 5-89. Zbl0615.22008MR849651
10. [Fa] M. Falk: On the algebra associated with a geometric lattice. Advances in Mathematics, vol. 80(2) ((1990) 152-163. Zbl0733.05026MR1046688
11. [Ge] I.M. Gelfand: General theory of hypergeometric functions. Soviet Math. Doklady33 (1986) 573-577. Zbl0645.33010MR841131
12. [Go-Mac] M. Goresky and R. MacPherson: Stratified Morse Theory, Ergebnisse der Mathematik und ihre Grenzgebiete, 3Folge, Band 14. Springer-Verlag, Berlin (1988). Zbl0639.14012MR932724
13. [Hi] F. Hirzzebriech: Arrangements of lines and algebraic surfaces, in "Arithmetic and Geometry", vol. II. Progress in Math. 36. Birkhauser, Boston (1983) 113-140. Zbl0527.14033MR717609
14. [Ji-Ya] T. Jiang and S.S.-T. Yau: Topological and differentiable structures of the complement of an arrangement of hyperplanes (preprint). MR1216551
15. [Ma] J. Mather: Notes on topological stability. Harvard University, July 1970. 
16. [Mo] B. Moishezon: Simply connected algebraic surfaces of general type. Invent. Math.89 (1987) 601-643. Zbl0627.14019MR903386
17. [Or1] P. Orlik: Introduction to Arrangements, C.B.M.S. Regional Conference Series in Mathematics, No. 72, A.M.S. Zbl0722.51003
18. [Or2] P. Orlik: Complements of subspace arrangements (preprint). Zbl0795.52003MR1129843
19. [Or-So1] P. Orlik and L. Solomon: Combinations and topology of complements of hyperplanes. Invent. Math.56 (1980) 167-189. Zbl0432.14016MR558866
20. [Or-So2] P. Orlik and L. Solomon: Unitary reflection groups and cohomology. Invent. Math.59 (1980) 77-94. Zbl0452.20050MR575083
21. [Or-So3] P. Orlik and L. Solomon: Discriminants in the invariant theory of reflection groups. Bagoya Math. J..109 (1988) 23-45. Zbl0614.20032MR931949
22. [Ra1] R. Randall: The fundamental group of the complement of a union of complex hyperplanes. Invent. Math.80 (1985) 467-468. A correction of this paper by the same author is in Invent. Math.80 (1985) 467-468. Zbl0596.14014MR791670
23. [Ra2] R. Randall: Lattice-isotopic arrangements are topologically isomorphic. Zbl0681.57016
24. [Sa1] M. Salvetti: Topology of the complement of real hyperplanes in CN. Invent. Math.88 (1987) 603-618. Zbl0594.57009MR884802
25. [Sa2] M. Salvetti: Arrangements of lines and monodromy of plane curves. Compositio Math.68 (1988) 103-122. Zbl0661.14038MR962507
26. [Sa3] M. Salvetti: On the homotopy theory of complexes associated to metrical-hemisphere complexes. Discrete Mathematics113 (1993) 155-177. Zbl0774.52007MR1212876
27. [Sh-To] G.C. Shepherd and J.A. Todd: Finite unitary reflection groups. Canad. J. Math.6 (1954) 274-304. Zbl0055.14305MR59914
28. [Te] B. Teissier: Cycles évanescents, sections planes et conditions de Whitney. Asterisque (Société Mathématique de France) No. 7-8, 1973. Zbl0295.14003MR374482

1. Fedor Bogomolov, Viktor Kulikov, On the diffeomorphic type of the complement to a line arrangement in a projective plane
2. Tan Jiang, Stephen S.-T. Yau, Intersection lattices and topological structures of complements of arrangements in ${\mathrm{ℂ\mathbb{P}}}^2$