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Uspekhi Mat. Nauk, 2001, Volume 56, Issue 2(338), Pages 167–203 (Mi umn384)  

This article is cited in 8 scientific papers (total in 8 papers)

Topology of plane arrangements and their complements

V. A. Vassiliev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper is a glossary of notions and methods related to the topological theory of affine plane arrangements, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of graphs, Orlik–Solomon rings, Salvetti complexes, matroids, Spanier–Whitehead duality, twisted homology groups, monodromy theory, and multidimensional hypergeometric functions. The emphasis is upon making the presentation as geometric as possible. Applications and analogies in differential topology are outlined, and some recent results of the theory are presented.

DOI: https://doi.org/10.4213/rm384

Full text: PDF file (546 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2001, 56:2, 365–401

Bibliographic databases:

Document Type: Article
UDC: 514.14
MSC: Primary 52C35, 57N65; Secondary 32S22, 05B35, 33C70, 14M15, 55R80, 55P25, 58K10, 2
Received: 06.03.2001

Citation: V. A. Vassiliev, “Topology of plane arrangements and their complements”, Uspekhi Mat. Nauk, 56:2(338) (2001), 167–203; Russian Math. Surveys, 56:2 (2001), 365–401

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Katz G., “How tangents solve algebraic equations, or a remarkable geometry of discriminant varieties”, Expo. Math., 21:3 (2003), 219–261  crossref  mathscinet  zmath  isi
    2. Vassiliev V.A., “Combinatorial formulas for cohomology of spaces of knots”, Advances in Topological Quantum Field Theory, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 179, 2004, 1–21  mathscinet  zmath  isi
    3. Kalai G., “Intersections of Leray complexes and regularity of monomial ideals”, J. Combin. Theory Ser. A, 113:7 (2006), 1586–1592  crossref  mathscinet  zmath  isi  elib  scopus
    4. Karasev R.N., “The genus and the category of configuration spaces”, Topology Appl., 156:14 (2009), 2406–2415  crossref  mathscinet  zmath  isi  elib  scopus
    5. Yu. V. Èliyashev, “The homology and cohomology of the complements to some arrangements of codimension two complex planes”, Siberian Math. J., 52:3 (2011), 554–562  mathnet  crossref  mathscinet  isi
    6. Yury V. Eliyashev, “The Hodge filtration on complements of complex subspace arrangements and integral representations of holomorphic functions”, Zhurn. SFU. Ser. Matem. i fiz., 6:2 (2013), 174–185  mathnet
    7. Yury V. Eliyashev, “Mixed Hodge structure on complements of complex coordinate subspace arrangements”, Mosc. Math. J., 16:3 (2016), 545–560  mathnet  mathscinet
    8. Okounkov A., “Enumerative Geometry and Geometric Representation Theory”, Algebraic Geometry: Salt Lake City 2015, Pt 1, Proceedings of Symposia in Pure Mathematics, 97, no. 1, eds. DeFernex T., Hassett B., Mustata M., Olsson M., Popa M., Thomas R., Amer Mathematical Soc, 2018, 419–457  crossref  mathscinet  isi
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