2017
DOI: 10.1016/j.topol.2017.04.027
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A Golod complex with non-suspension moment-angle complex

Abstract: Abstract. It could be expected that the moment-angle complex associated with a Golod simplicial complex is homotopy equivalent to a suspension space. In this paper, we provide a counter example to this expectation. We have discovered this complex through the studies of the Golod property of the Alexander dual of a join of simplicial complexes, and that of a union of simplicial complexes.

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Cited by 10 publications
(9 citation statements)
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“…See a survey [4] for more information about moment-angle complexes and polyhedral products. Here we remark that there is a Golod complex K such that Z K is not a suspension as shown by Yano and the first author [20].…”
Section: Introductionmentioning
confidence: 70%
“…See a survey [4] for more information about moment-angle complexes and polyhedral products. Here we remark that there is a Golod complex K such that Z K is not a suspension as shown by Yano and the first author [20].…”
Section: Introductionmentioning
confidence: 70%
“…Consider the space Y (RC ′ K ), constructed as in (10). According to the Lyndon Identity Theorem, Y (RC ′ K ) is homotopy equivalent to K(RC ′ K , 1), so its homology groups coincide with the homology groups of the space R K .…”
Section: One-relator Groupsmentioning
confidence: 99%
“…For non-flag K, all homotopy-theoretical characterisations of moment-angle complexes Z K are more complex. For example, for an arbitrary Golod complex K, the moment-angle complex Z K is not necessarily a co-H space [10] and its cohomology can contain torsion [7]. Furthermore, describing the Pontryagin algebra H * (ΩZ K ), and in particular determining the class of K for which it is a free or one-relator algebra, is considerably harder in the non-flag case.…”
Section: Introductionmentioning
confidence: 99%
“…K. Iriye and T. Yano [84], also take the approach of desuspending (13.4). They use a simplicial complex constructed from a triangulated Hopf map η : S 3 → S 2 , and Alexander duality to prove the existence of a simplicial complex K for which k(K) is a Golod ring but Z(K; (D 2 , S 1 )) is not a suspension.…”
Section: Polyhedral Products and The Golodness Of Monomial Ideal Ringsmentioning
confidence: 99%