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

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(BT). 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 H2(BT) adapted to the isotropy groups occurring in a given T–space.

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equivariant cohomology, syzygy, big polygon space
Mathematical Subject Classification 2010
Primary: 55N91
Secondary: 13D02, 55R80
Received: 20 June 2019
Accepted: 10 October 2019
Published: 4 November 2020
Matthias Franz
Department of Mathematics
University of Western Ontario
London ON
Jianing Huang
Department of Mathematics
University of Western Ontario
London ON