A Cohomological Obstruction to the Existence of $ϕ$-Equivariant Maps

Let $ϕ: G\to H$ be a continuous homomorphism between compact Lie groups, let $X$ be a $G$-space, and let $Y$ be an $H$-space. We formulate a filtered change-of-groups obstruction to the existence of a $ϕ$-equivariant map $X\to Y$. We apply them to the inclusion of a finite cyclic group into the circ