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Uspekhi Mat. Nauk, 2001, Volume 56, Issue 2(338), Pages 87–166 (Mi umn383)  

This article is cited in 48 scientific papers (total in 48 papers)

Orlik–Solomon algebras in algebra and topology

S. A. Yuzvinskii

University of Oregon

Abstract: This is a survey of Orlik–Solomon algebras of hyperplane arrangements. These algebras first appeared in theorems due to Arnol'd, Brieskorn, and Orlik and Solomon as the cohomology algebras of the complements of complex hyperplane arrangements. 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. 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 by Orlik and Terao. For some of these facts new and more straightforward or shorter proofs are given.

DOI: https://doi.org/10.4213/rm383

Full text: PDF file (820 kB)
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English version:
Russian Mathematical Surveys, 2001, 56:2, 293–364

Bibliographic databases:

UDC: 512.66
MSC: Primary 52C35, 05B35, 16S37; Secondary 14F40, 32S22, 16E05, 13P10
Received: 25.09.2000

Citation: S. A. Yuzvinskii, “Orlik–Solomon algebras in algebra and topology”, Uspekhi Mat. Nauk, 56:2(338) (2001), 87–166; Russian Math. Surveys, 56:2 (2001), 293–364

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    This publication is cited in the following articles:
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