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We study Cohen–Macaulay actions, a class of torus actions on manifolds, possibly without fixed points, which generalizes and has analogous properties as equivariantly formal actions. Their equivariant cohomology algebras are computable in the sense that a Chang–Skjelbred Lemma, and its stronger version, the exactness of an Atiyah–Bredon sequence, hold. The main difference is that the fixed‐point set is replaced by the union of lowest dimensional orbits. We find sufficient conditions for the Cohen–Macaulay property such as the existence of an invariant Morse–Bott function whose critical set is the union of lowest dimensional orbits, or open‐face‐acyclicity of the orbit space. Specializing to the case of torus manifolds, that is, 2 r ‐dimensional orientable compact manifolds acted on by  r ‐dimensional tori, the latter is similar to a result of Masuda and Panov, and the converse of the result of Bredon that equivariantly formal torus manifolds are open‐face‐acyclic.

Torus actions whose equivariant cohomology is Cohen–Macaulay