Transformation Groups

, Volume 22, Issue 4, pp 933–965 | Cite as


  • MATTHIAS FRANZEmail author


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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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Western OntarioLondonCanada

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