TY - JOUR
T1 - Integral cohomology groups of real toric manifolds and small covers
AU - Cai, Li
AU - Choi, Suyoung
N1 - Publisher Copyright:
© 2021 Independent University of Mosow.
PY - 2021/7/1
Y1 - 2021/7/1
N2 - For a simplicial complex K with m vertices, there is a canonical Zm2-space known as a real moment angle complex RZK. In this paper, we consider the quotient spaces Y = RZK/Zk2, where K is a pure shellable complex and Zk2 ⊂ Zm2 is a maximal free action on RZK. 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.
AB - For a simplicial complex K with m vertices, there is a canonical Zm2-space known as a real moment angle complex RZK. In this paper, we consider the quotient spaces Y = RZK/Zk2, where K is a pure shellable complex and Zk2 ⊂ Zm2 is a maximal free action on RZK. 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.
KW - Bockstein homo-morphisms
KW - Cohomology groups
KW - Real toric manifold
KW - Small cover
UR - http://www.scopus.com/inward/record.url?scp=85108944183&partnerID=8YFLogxK
U2 - 10.17323/1609-4514-2021-21-3-467-492
DO - 10.17323/1609-4514-2021-21-3-467-492
M3 - Article
AN - SCOPUS:85108944183
SN - 1609-3321
VL - 21
SP - 467
EP - 492
JO - Moscow Mathematical Journal
JF - Moscow Mathematical Journal
IS - 3
ER -