Finitistic Spaces with Orbit Space a Product of Projective Spaces

Abstract

Let G = Z2 act freely on a finitistic space X. If the mod 2 cohomology of X is isomorphic to the real projective space RP2n+1(resp. complex projective space CP2n+1) then the mod 2 cohomology of orbit spaces of these free actions are RP1 xCPn(resp. RP2xHPn) [11]. In this paper, we have discussed converse of this result. We have showed that if the mod 2 cohomology of the orbit space X/G is RP1xCPn(resp. RP2 x HPn). Similar, results for p > 2, a prime, is also discussed. It is proved that one of the possibilities of orbit spaces of free involutions on product of projective spaces RPn x RP2m+1(resp. CPn x CP2m+1) is RP1 x RPn x CPm(resp. RP2 x CPn x HPm) [12]. The converse of these statements are also discussed