On the cohomology ring of hyperplane complements

Jozsa, Richard; Rice, John

doi:10.1090/S0002-9939-1991-1065085-5

On the cohomology ring of hyperplane complements
HTML articles powered by AMS MathViewer

by Richard Jozsa and John Rice PDF

Proc. Amer. Math. Soc. 113 (1991), 973-981 Request permission

Abstract:

Using only the long exact sequence of local cohomology, we give a brief derivation of Orlik and Solomon’s presentation for the cohomology ring of a complement of hyperplanes in a vector space.

References

Raoul Bott and Loring W. Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics, vol. 82, Springer-Verlag, New York-Berlin, 1982. MR 658304
Egbert Brieskorn, Sur les groupes de tresses [d’après V. I. Arnol′d], Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 401, Lecture Notes in Math., Vol. 317, Springer, Berlin, 1973, pp. 21–44 (French). MR 0422674
Birger Iversen, Cohomology of sheaves, Universitext, Springer-Verlag, Berlin, 1986. MR 842190, DOI 10.1007/978-3-642-82783-9
Peter Orlik, Introduction to arrangements, CBMS Regional Conference Series in Mathematics, vol. 72, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1989. MR 1006880, DOI 10.1090/cbms/072
Peter Orlik and Louis Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), no. 2, 167–189. MR 558866, DOI 10.1007/BF01392549
Peter Orlik, Louis Solomon, and Hiroaki Terao, Arrangements of hyperplanes and differential forms, Combinatorics and algebra (Boulder, Colo., 1983) Contemp. Math., vol. 34, Amer. Math. Soc., Providence, RI, 1984, pp. 29–65. MR 777693, DOI 10.1090/conm/034/777693