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Betti Numbers of Small Covers and Their Two-Fold Coverings

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Abstract

We compute the Betti numbers of two-fold coverings of small covers with some special properties; in particular, we use the results of Davis and Januszkiewicz on the cohomology of small covers. It turned out that their proof contains some gap that we describe in detail and fill in.

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References

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Authors and Affiliations

  1. Moscow State University, Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

    D. S. Ulyumdzhiev

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  1. D. S. Ulyumdzhiev
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Correspondence to D. S. Ulyumdzhiev.

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Original Russian Text Copyright © 2018 Ulyumdzhiev D.S.

The author was supported by the President of the Russian Federation (Grant MD–2907.2017.1) and the Russian Foundation for Basic Research (Grant 18–51–50005).

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, vol. 59, no. 3, pp. 696–701, May–June, 2018

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Ulyumdzhiev, D.S. Betti Numbers of Small Covers and Their Two-Fold Coverings. Sib Math J 59, 551–555 (2018). https://doi.org/10.1134/S0037446618030175

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  • DOI: https://doi.org/10.1134/S0037446618030175

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