Betti numbers of small covers and their two-fold coverings

D. S. Ulyumdzhiev<sup>ab

a</sup> Lomonosov Moscow State University, Moscow, Russia
^b Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

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.

Keywords: simple polyhedron, small cover, two-fold covering, cohomology of two-fold coverings.

UDC: 515.146.39

MSC: 35R30

Received: 22.09.2017

DOI: 10.17377/smzh.2018.59.317

 English version: Siberian Mathematical Journal, 2018, 59:3, 551–555

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