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Funktsional. Anal. i Prilozhen., 2001, Volume 35, Issue 2, Pages 3–11 (Mi faa241)  

This article is cited in 11 scientific papers (total in 11 papers)

Classification Problem for Quasitoric Manifolds over a Given Simple Polytope

N. E. Dobrinskaya

M. V. Lomonosov Moscow State University

Abstract: The classification problem for quasitoric manifolds over a given polytope $P^n$ is considered. The known construction of weights, which was used in the study of the similar problem for toric manifolds, is modified. The construction thus obtained is applied to the solution of the above problem in small dimensions. Classification results are also obtained for polytopes that are products of finitely many simplices of arbitrary dimensions.

DOI: https://doi.org/10.4213/faa241

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English version:
Functional Analysis and Its Applications, 2001, 35:2, 83–89

Bibliographic databases:

UDC: 515.16
Received: 26.10.1999

Citation: N. E. Dobrinskaya, “Classification Problem for Quasitoric Manifolds over a Given Simple Polytope”, Funktsional. Anal. i Prilozhen., 35:2 (2001), 3–11; Funct. Anal. Appl., 35:2 (2001), 83–89

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Buchstaber, T. E. Panov, “Torus actions, combinatorial topology, and homological algebra”, Russian Math. Surveys, 55:5 (2000), 825–921  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. T. E. Panov, “Hirzebruch genera of manifolds with torus action”, Izv. Math., 65:3 (2001), 543–556  mathnet  crossref  crossref  mathscinet  zmath  elib
    3. M. Masuda, T. E. Panov, “Semifree circle actions, Bott towers and quasitoric manifolds”, Sb. Math., 199:8 (2008), 1201–1223  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Choi, S, “The number of small covers over cubes”, Algebraic and Geometric Topology, 8:4 (2008), 2391  crossref  mathscinet  zmath  isi  scopus
    5. Buchstaber V.M., Ray N., “An invitation to toric topology: Vertex four of a remarkable tetrahedron”, Toric Topology, Contemporary Mathematics Series, 460, 2008, 1–27  crossref  mathscinet  zmath  isi
    6. Buchstaber V., Panov T., Ray N., “Toric Genera”, Int Math Res Not, 2010, no. 16, 3207–3262  mathscinet  zmath  isi  elib
    7. Choi S., Masuda M., Suh D.Y., “Quasitoric Manifolds Over a Product of Simplices”, Osaka J Math, 47:1 (2010), 109–129  mathscinet  zmath  isi  elib
    8. Proc. Steklov Inst. Math., 275 (2011), 177–190  mathnet  crossref  mathscinet  isi  elib  elib
    9. Choi S., Park S., Suh D.Y., “Topological Classification of Quasitoric Manifolds with Second Betti Number 2”, Pac. J. Math., 256:1 (2012), 19–49  crossref  mathscinet  zmath  isi  elib  scopus
    10. Choi S., Park H., “Wedge operations and torus symmetries”, Tohoku Math. J., 68:1 (2016), 91–138  crossref  mathscinet  zmath  isi  elib  scopus
    11. Choi S., Park S., “Projective bundles over toric surfaces”, Int. J. Math., 27:4 (2016), 1650032  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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