Moment-angle complexes from simplicial posets

• Autorzy: Zhi Lü , Taras Panov
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Moment-angle complex; Simplicial poset; Simplicial complex; Torus action; Face ring; Stanley-Reisner ring; Toral rank

Kategorie tematyczne

• 14M25: Toric varieties, Newton polyhedra
• 57S15: Compact Lie groups of differentiable transformations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 715-730

Daty

wydano

2011-08-01

online

2011-05-26

Twórcy

autor

Zhi Lü

• Fudan University

autor

Taras Panov

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0041-z