Freeness of equivariant cohomology and mutants of compactified representations

Abstract

We survey generalisations of the Chang-Skjelbred Lemma for integral coefficients. Moreover, we construct examples of manifolds with actions of tori of rank > 2 whose equivariant cohomology is torsion-free, but not free. This answers a question of Allday's. The "mutants" we construct are obtained from compactified representations and involve Hopf bundles in a crucial way.

11 pages; more details on the smooth structure of the mutants; other, minor changes

References in corpus (3)

• Koszul duality and equivariant cohomology for tori
• The equivariant cohomology of weighted projective space
• On the cohomology rings of Hamiltonian T-spaces

Cited by in corpus (9)

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• Moment Angle Complexes and Big Cohen-Macaulayness
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• Big polygon spaces
• How is a graph not like a manifold?
• Mutants of compactified representations revisited
• The syzygy order of big polygon spaces
• Equivariant de Rham Cohomology: Theory and Applications