On the cohomology and their torsion of real toric objects
On the cohomology and their torsion of real toric objects
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DOI：
10.1515/forum-2016-0025
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发表时间：
2013-11
期刊：
影响因子：
--
通讯作者：
Suyoung Choi;Hanchul Park
中科院分区：
文献类型：
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作者：
Suyoung Choi;Hanchul Park
在本文中，我们做了这两件事。1.给出了一个计算实拓扑环流形的有理上同调环的公式，从而得到了小覆盖或实环面流形的有理上同调环的计算公式，它包含了Suciu和Trevisan的公式。此外，该公式还适用于其他系数$\mathbb{Z}_q=\mathbb{Z}/q\mathbb{Z}$，其中$q$为正的奇数。2.我们构造了无穷多个实环面流形和小覆盖，它们的积分上同调对任意正奇数$q$都有$q$-挠。
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 $q$.