Far Eastern Mathematical Journal

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Families of minimally non-Golod simplicial complexes and polyhedral products

Limonchenko I.Yu.

2015, issue 2, . 222-237

We consider families of simple polytopes P and simplicial complexes K well-known in polytope theory and convex geometry, and show that their moment-angle complexes have some remarkable homotopy properties which depend on combinatorics of the underlying complexes and algebraic properties of their Stanley-Reisner rings. We introduce infinite series of Golod and minimally non-Golod simplicial complexes K with moment-angle complexes k having free integral cohomology but not homotopy equivalent to a wedge of spheres or a connected sum of products of spheres respectively. We then prove a criterion for a simplicial multiwedge and composition of complexes to be Golod and minimally non-Golod and present a class of minimally non-Golod polytopal spheres.

simple polytopes, Golod rings, moment-angle complexes, Stanley-Reisner rings

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