The syzygy order of big polygon spaces

Franz, Matthias; Huang, Jianing

doi:10.2140/agt.2020.20.2657

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The syzygy order of big polygon spaces

Matthias Franz and Jianing Huang

Algebraic & Geometric Topology 20 (2020) 2657–2675

DOI: 10.2140/agt.2020.20.2657

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 $H^{*} (B T)$ . 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 $H^{2} (B T)$ 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

References

Publication

Received: 20 June 2019

Accepted: 10 October 2019

Published: 4 November 2020

Authors

Matthias Franz
Department of Mathematics University of Western Ontario London ON Canada

Jianing Huang
Department of Mathematics University of Western Ontario London ON Canada

Volume 20, issue 5 (2020)