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Equivariant classification of 2-torus manifolds

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Lü Z., Masuda M.

Colloquium Mathematicum

2009

tom 115

nr 2

171-188

We consider locally standard 2-torus manifolds, which are a generalization of small covers of Davis and Januszkiewicz and study their equivariant classification. We formulate a necessary and sufficient condition for two locally standard 2-torus manifolds over the same orbit space to be equivariantly homeomorphic. This leads us to count the equivariant homeomorphism classes of locally standard 2-torus manifolds with the same orbit space.

Moment-angle complexes from simplicial posets

100%

Lü Z., Panov T.

Open Mathematics

2011

tom 9

nr 4

715-730

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Open Mathematics

2 Lü Z.

1 Masuda M.

1 Panov T.

1 2011

1 2009

Wyniki wyszukiwania

Equivariant classification of 2-torus manifolds

Moment-angle complexes from simplicial posets