#### Volume 20, issue 5 (2020)

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The syzygy order of big polygon spaces

### Matthias Franz and Jianing Huang

Algebraic & Geometric Topology 20 (2020) 2657–2675
##### Abstract

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 ${H}^{\ast }\left(BT\right)$. 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 ${H}^{2}\left(BT\right)$ adapted to the isotropy groups occurring in a given $T$–space.

##### Keywords
equivariant cohomology, syzygy, big polygon space
##### Mathematical Subject Classification 2010
Primary: 55N91
Secondary: 13D02, 55R80