We extend the construction of moment-angle complexes to simplicial posets by associating a certain T m-space Z S to an arbitrary simplicial poset S on m vertices. Face rings ℤ[S] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and Cohen-Macaulay rings. Our primary motivation is to study the face rings ℤ[S] by topological methods. The space Z S has many important topological properties of the original moment-angle complex Z K associated to a simplicial complex K. In particular, we prove that the integral cohomology algebra of Z S is isomorphic to the Tor-algebra of the face ring ℤ[S]. This leads directly to a generalisation of Hochster’s theorem, expressing the algebraic Betti numbers of the ring ℤ[S] in terms of the homology of full subposets in S. Finally, we estimate the total amount of homology of Z S from below by proving the toral rank conjecture for the moment-angle complexes Z S.
@article{bwmeta1.element.doi-10_2478_s11533-011-0041-z,
author = {Zhi L\"u and Taras Panov},
title = {Moment-angle complexes from simplicial posets},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {715-730},
zbl = {1236.57045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0041-z}
}
Zhi Lü; Taras Panov. Moment-angle complexes from simplicial posets. Open Mathematics, Tome 9 (2011) pp. 715-730. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0041-z/
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