The Borel localization theorem in (Borel) equivariant cohomology states that if $T$ is a torus and $M$ a smooth $T$-manifold, with fixed point set $M^T$, then upon localizing the coefficient ring $H^*_T := H^*(BT)$ (that is, tensoring with its field of fractions), the restriction map $$H^*_T(M) \to H^*_T(M^T)$$ becomes an isomorphism.

The earliest reference to this result I know of is in Hsiang Wu-Yi's classic book on transformation groups, where he refers to the result as a "localization theorem of Borel–Atiyah–Segal type." It seems from Hsiang's presentation that Borel only proved this result for $T = S^1$; in any event, I've never been able to find the more general result in the Seminar on Transformation Groups. But I'd like to attribute it to someone.

Who originated this result? Failing back, what is the earliest citation you know?

The Borel localization theorem in (Borel) equivariant cohomology states that if $T$ is a torus and $M$ a smooth $T$-manifold, with fixed point set $M^T$, then upon localizing the coefficient ring $H^*_T := H^*(BT)$ (that is, tensoring with its field of fractions), the restriction map $$H^*_T(M) \to H^*_T(M^T)$$ becomes an isomorphism.

The earliest reference to this result I know of is in Hsiang Wu-Yi's classic book on transformation groups, where he refers to the result as a "localization theorem of Borel–Atiyah–Segal type." It seems from Hsiang's presentation that Borel only proved this result for $T = S^1$; in any event, I've never been able to find the more general result in the Seminar on Transformation Groups. But I'd like to attribute it to someone.

Who originated this result? Failing that, what is the earliest citation you know?