THREE-DIMENSIONAL MANIFOLDS, SKEW-GORENSTEIN RINGS AND THEIR COHOMOLOGY

Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra). We present some applications of the homological theory of these graded skew-commutative rings. In particular, we find compact oriented 3-manifolds without boundary for which the Hilbert series of the Yoneda Ext-algebra of the cohomology ring of the fundamental group is an explicit transcendental function. This is only possible for large first Betti numbers of the 3-manifold (bigger than, or maybe equal to, 11). We give also examples of 3-manifolds where the Ext-algebra of the cohomology ring of the fundamental group is not finitely generated.