Abstract
Let X be a manifold with an action of a torus T such that all isotropy groups are connected and satisfying some other mild hypotheses. We provide a necessary and sufficient criterion for the equivariant cohomology H * T (X) with real coefficients to be a certain syzygy as module over H*(BT). It turns out that, possibly after blowing up the non-free part of the action, this only depends on the orbit space X/T together with its stratification by orbit type. Our criterion unifies and generalizes results of many authors about the freeness and torsion-freeness of equivariant cohomology for various classes of T-manifolds.
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05 April 2019
We correct a mistake in Proposition 3.3 of the paper. All other results remain unchanged.
05 April 2019
We correct a mistake in Proposition 3.3 of the paper. All other results remain unchanged.
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*Supported by an NSERC Discovery Grant.
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FRANZ, M. A QUOTIENT CRITERION FOR SYZYGIES IN EQUIVARIANT COHOMOLOGY. Transformation Groups 22, 933–965 (2017). https://doi.org/10.1007/s00031-016-9408-3
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DOI: https://doi.org/10.1007/s00031-016-9408-3