Big polygon spaces are compact orientable manifolds with a torus action whose equivariant cohomology can be torsion-free or reflexive without being free as a module over . We determine the exact syzygy order of the equivariant cohomology of a big polygon space as a function of the length vector defining it. The proof uses a refined characterization of syzygies in terms of certain linearly independent elements in adapted to the isotropy groups occurring in a given –space.
"The syzygy order of big polygon spaces." Algebr. Geom. Topol. 20 (5) 2657 - 2675, 2020. https://doi.org/10.2140/agt.2020.20.2657