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Orlik-Solomon algebras in algebra and topology

机译:代数和拓扑中的Orlik-Solomon代数

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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. [References: 71]
机译:这是超平面排列的Orlik-Solomon代数的一项调查。这些代数首先出现在定理中,这是由于Arnol'd,Brieskorn以及Orlik和Solomon作为复杂超平面排列的补充的同调代数。随后发现了这些代数的许多应用。该调查仅限于研究Orlik-Solomon代数本身及其在拓扑和组合学中的一些应用。大多数结果来自最近的论文和预印本,尽管为了读者的方便,我们也从Orlik和Terao的《超飞机的安排》一书中包括了相关的定义和基本事实。对于其中的某些事实,给出了新的,更直接的或更短的证明。 [参考:71]

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