Abstract: This is the last part of the syzygy saga (but independent of the previous talks).

I will recall how syzygies interpolate between torsion-free and free modules and why certain syzygies are ruled out in the torus-equivariant cohomology of compact orientable manifolds. More precisely, by a result of Allday, Puppe and myself there is a bound on the syzygy order unless the equivariant cohomology is free. The main point of this talk is to show that this bound is sharp. I will do so by exhibiting a new class compact orientable manifolds with torus action. These manifolds are related to polygon spaces as studied by Hausmann, Farber and many others.

Abstract: