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January 2019 On Hochster's formula for a class of quotient spaces of moment-angle complexes
Li Yu
Osaka J. Math. 56(1): 33-50 (January 2019).

Abstract

Any finite simplicial complex $\mathcal{K}$ and a partition of the vertex set of $\mathcal{K}$ determines a canonical quotient space of the moment-angle complex of ${\mathcal K}$. We prove that the cohomology groups of such a space can be computed via some Hochster's type formula, which generalizes the usual Hochster's formula for the cohomology groups of moment-angle complexes. In addition, we show that the stable decomposition of moment-angle complexes can also be extended to such spaces. This type of spaces include all the quasitoric manifolds that are pullback from the linear models. And we prove that the moment-angle complex associated to a finite simplicial poset is always homotopy equivalent to one of such spaces.

Citation

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Li Yu. "On Hochster's formula for a class of quotient spaces of moment-angle complexes." Osaka J. Math. 56 (1) 33 - 50, January 2019.

Information

Published: January 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07055397
MathSciNet: MR3908775

Subjects:
Primary: 14M25 , 57S15

Rights: Copyright © 2019 Osaka University and Osaka City University, Departments of Mathematics

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Vol.56 • No. 1 • January 2019
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