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Article overview
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Cohomology rings of moment-angle complexes | Feifei Fan
; Xiangjun Wang
; | Date: |
1 Aug 2015 | Abstract: | Associated to every finite simplicial complex $K$, there is a moment-angle
complex $mathcal {Z}_{K}$; $mathcal {Z}_{K}$ is a compact manifold if and
only if $|K|$ is a generalized homology sphere. The main goal of this article
is to study the cohomology rings of moment-angle complexes associated to some
special simplicial complexes.
First, we give the cohomological transformation formulae of $mathcal
{Z}_{K}$ induced by some combinatorial operations on the base space $K$, such
as the connected sum operation on Gorenstein* complexes and the stellar
subdivisions on simplicial spheres. Second, we prove the indecomposable
property of $mathcal {Z}_{K}$ (i.e. $mathcal {Z}_{K}$ is a prime manifold)
when $K$ is a flag $2$-sphere by proving the indecomposable property of their
cohomology rings. Then we use these results to solve the cohomological rigidity
problem for some moment-angle manifolds and the $B$-rigidity problem for some
simplicial spheres. | Source: | arXiv, 1508.0159 | Services: | Forum | Review | PDF | Favorites |
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