Orlik-Solomon algebras in algebra and topology (Q2784555)

The paper is a very nice survey of Orlik-Solomon algebras (of hyperplane arrangements). These algebras first appeared in theorems due to \textit{V. I. Arnol'd} [Math. Notes 5, 138--140 (1969); translation from Mat. Zametki 5, 227--231 (1969; Zbl 0277.55002)], \textit{E. Brieskorn} [Lect. Notes Math. 317, 21--44 (1973; Zbl 0277.55003)] and \textit{P. Orlik} and \textit{L. Solomon} as the cohomology algebras of the complements of complex hyperplane arrangements [Invent. Math. 56, 167--189 (1980; Zbl 0432.14016)].NEWLINENEWLINE Numerous applications of these algebras have subsequently been found. This survey is confined to studying Orlik-Solomon algebras per se and some of their applications to topology and combinatorics.NEWLINENEWLINEFrom the text: Most of the results are taken from recent papers and preprints, although for the reader's convenience we also include relevant definitions and basic facts from the book [Arrangements of hyperplanes (1992; Zbl 0757.55001)] by \textit{P. Orlik} and \textit{H. Terao}. For some of these facts new and more straightforward or shorter proofs are given.