Circle group action on the product of two projective spaces (Q2800395)

Supose that the group \(G = \mathbb{S}^1\) act freely on a finitistic space \(X\) with mod 2 cohomology ring isomorphic to that of the product of two real projective spaces. In the paper under review, the authors compute the mod 2 cohomology algebra of the orbit space \(X/G\). They also show that \(G\) cannot act freely on the mod 2 product of two complex projective spaces. The main tool used is the Leray-Serre spectral sequence associated to the Borel fibration.