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This article is cited in 3 scientific papers (total in 3 papers)
Integral cohomology groups of real toric manifolds and small covers
Li Caia, Suyoung Choib a Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, Suzhou 215123, Jiangsu, China
b Department of Mathematics, Ajou University, 206 Worldcup-ro, Suwon 16499, South Korea
Abstract:
For a simplicial complex $K$ with $m$ vertices, there is a canonical $\mathbb{Z}_2^m$-space known as a real moment angle complex $\mathbb{R}\mathcal{Z}_K$. In this paper, we consider the quotient spaces $Y=\mathbb{R}\mathcal{Z}_K /\mathbb{Z}_2^{k}$, where $K$ is a pure shellable complex and $\mathbb{Z}_2^k \subset\mathbb{Z}_2^m$ is a maximal free action on $\mathbb{R}\mathcal{Z}_K$. A typical example of such spaces is a small cover, where a small cover is known as a topological analog of a real toric manifold. We compute the integral cohomology group of $Y$ by using the PL cell decomposition obtained from a shelling of $K$. In addition, we compute the Bockstein spectral sequence of $Y$ explicitly.
Key words and phrases:
real toric manifold, small cover, Bockstein homomorphisms, Cohomology groups.
Citation:
Li Cai, Suyoung Choi, “Integral cohomology groups of real toric manifolds and small covers”, Mosc. Math. J., 21:3 (2021), 467–492
Linking options:
https://www.mathnet.ru/eng/mmj802 https://www.mathnet.ru/eng/mmj/v21/i3/p467
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Abstract page: | 65 | References: | 15 |
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