# Golodness and polyhedral products of simplicial complexes with minimal Taylor resolutions

@article{Iriye2018GolodnessAP,
title={Golodness and polyhedral products of simplicial complexes with minimal Taylor resolutions},
author={Kouyemon Iriye and Daisuke Kishimoto},
journal={Homology, Homotopy and Applications},
year={2018},
volume={20},
pages={69-78}
}
• Published 2018
• Mathematics
• Homology, Homotopy and Applications
Let K be a simplicial complex such that the Taylor resolution for its Stanley-Reisner ring is minimal. We prove that the following conditions are equivalent: (1) K is Golod; (2) any two minimal non-faces of K are not disjoint; (3) the moment-angle complex for K is homotopy equivalent to a wedge of spheres; (4) the decomposition of the suspension of the polyhedral product ZK(CX,X) due to Bahri, Bendersky, Cohen and Gitler desuspends.
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## References

SHOWING 1-10 OF 10 REFERENCES
Golodness and polyhedral products for two-dimensional simplicial complexes
• Mathematics
• 2015
Abstract Golodness of two-dimensional simplicial complexes is studied through polyhedral products, and combinatorial and topological characterizations of Golodness of surface triangulations are
Cellular cochain algebras and torus actions
• Mathematics
• 2004
. Cellular cochains do notadmit a functorial associative multiplication because a proper cellular diag-onal approximation does not exist in general. The construction of moment-angle complexes is a
Convex polytopes, Coxeter orbifolds and torus actions
• Mathematics
• 1991
0. Introduction. An n-dimensional convex polytope is simple if the number of codimension-one faces meeting at each vertex is n. In this paper we investigate certain group actions on manifolds, which
Convex Polytopes
• Mathematics
• 1967
Graphs, Graphs and Realizations Before proceeding to the graph version of Euler’s formula, some notation will be introduced. A (finite) abstract graph G consists of two sets, the set of vertices V =
The polyhedral product functor: a method of decomposition for moment-angle complexes
• arrangements and related spaces, Adv. Math. 225
• 2010