On the cohomology and their torsion of real toric objects

2013/11/27 by Choi, Suyoung, Park, Hanchul · 3 citations
#05E45 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary 57N65 #Secondary 57S17

paper · doi:10.48550/arxiv.1311.7056

Abstract

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 ℤ_q = ℤ/qℤ, 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.

Cited by

• On small covers over Bier spheres
• On the integral cohomology of real toric manifolds
• A decomposition of graph a-numbers

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