The notion of a Golod ring was introduced rstly in the work [4] for Noetherian local rings and is now a classical object of study in commutative algebra (homology of local rings). It appears in toric topology as a Stanley Reisner ring (or face ring) k[K] of a simplicial complex K over a ring of integers or a eld of zero characteristic k. Due to Buchstaber and Panov theorem on the cohomology ring of a moment-angle complex ZK [2] and the results of Berglund and Jollenbeck [1], it is just the case when multiplication in the ring H(ZK; k) is trivial. For some special classes of simplicial complexes in [6] and [5] it was shown that their face rings k[K] are Golod ones and in all those cases (if integer homology groups of all induced subcomplexes in K are torsion free) the corresponding moment-angle complexes have homotopy types of wedges of spheres.
In [1] the notion of a minimally non-Golod simplicial complex was introduced, that is k[K] is not Golod itself but deleting of any vertex from K turns the face ring into a Golod one. In my talk, based on [7], I will present some results to show that minimal non-Golodness of a face ring is in a close relation with the case when the simplicial complex is a boundary of a simplicial polytope. Moreover, for many of these polytopes (among them are the duals to vertex truncations of one or a product of two simplicies as well as even dimensional neighbourly polytopes, combinatorially dierent from simplices) a description of dieomorphism types of the corresponding moment-angle manifolds is well known in toric topology [3]. These manifolds are connected sums of sphere products with two spheres in each product.

References:

[1] Alexander Berglund and Michael Jollenbeck. On the Golod property of Stanley Reisner rings, J. Algebra 315:1 (2007), 249-273.
[2] Victor M. Buchstaber and Taras E. Panov. Toric Topology, A book project (2013); arXiv:1210.2368.
[3] Samuel Gitler and Santiago Lopez de Medrano. Intersections of quadrics, moment-angle manifolds and connected sums, Preprint (2009); arXiv:0901.2580.
[4] Evgeniy S. Golod. On the cohomology of some local rings (Russian); Soviet Math. Dokl. 3 (1962), 745-749.
[5] Jelena Grbic, Taras Panov, Stephen Theriault and Jie Wu. Homotopy types of moment-angle complexes for ag complexes, Preprint (2012); arXiv:1211.0873.
[6] Jelena Grbic, Stephen Theriault. The homotopy type of the complement of a coordi-
nate subspace arrangement. Topology 46 (2007, no. 4, 357-396)
[7] Ivan Yu. Limonchenko. StanleyReisner rings of generalized truncation polytopes and their moment-angle manifolds. Proc. of the Steklov Math. Inst. (2014) (to appear); arXiv:1401.2124.