The syzygy order of big polygon spaces

Franz, Matthias¹ ; Huang, Jianing¹

¹Department of Mathematics, University of Western Ontario, London ON, Canada

Algebraic and Geometric Topology, Tome 20 (2020) no. 5, pp. 2657-2675

Résumé

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.

Détail

DOI : 10.2140/agt.2020.20.2657

Classification : 55N91, 13D02, 55R80
Keywords: equivariant cohomology, syzygy, big polygon space

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