Integral cohomology groups of real toric manifolds and small covers

2016/04/24 by Li Cai, Suyoung Choi, Cai, Li +1 · 3 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1604.06988

openalex publication_date 2016/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a simplicial complex K with m vertices, there is a canonical \mathbb Z₂^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 Z₂^k, where K is a pure shellable complex and \mathbb Z₂^k ⊂ \mathbb Z₂^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.

Citations

• On the cohomology of polyhedral products with space pairs (D¹, S⁰)

Cited by

• On the integral cohomology of real toric manifolds
• Cellular \mathbbA¹-Homology of Smooth Toric Varieties
• The cohomology groups of real toric varieties associated to Weyl chambers of type C and D

Related

• Multiplication structure of the cohomology ring of real toric spaces
• On the cohomology and their torsion of real toric objects
• Small covers over wedges of polygons
• On the integral cohomology of real toric manifolds
• Torus actions, combinatorial topology and homological algebra