On the cohomology and their torsion of real toric objects

By Suyoung Choi, Hanchul Park. 2013

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In this paper, we do the two things. 1. We present a formula to compute the rational cohomology ring of a real topological toric manifold, and thus that of a small cover or a real toric manifold, which implies the formula of Suciu and Trevisan. Furthermore, the formula also works for other coefficient $\mathbb{Z}_q = \mathbb{Z}/q\mathbb{Z}$, where $q$ is a positive odd integer. 2. We construct infinitely many real toric manifolds and small covers whose integral cohomology have a $q$-torsion for any positive odd integer $q$.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/a37398fadaf78bf2f0519dbd7061253e9b1c97cd