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# Equivariant Formality for Actions of Torus Groups

This paper contains a comparison of several definitions of equivariant formality for actions of torus groups. We develop and prove some relations between the definitions. Focusing on the case of the circle group, we use $S^1$-equivariant minimal models to give a number of examples of $S^1$-spaces illustrating the properties of the various definitions.
 MSC Classifications: 55P91 - Equivariant homotopy theory [See also 19L47] 55P62 - Rational homotopy theory 55R35 - Classifying spaces of groups and $H$-spaces 55S45 - Postnikov systems, $k$-invariants