Finitistic Spaces With The Orbit Space 𝔽ℙn × 𝕊m

Let Formula: see text, Formula: see text or Formula: see text, act freely on a finitistic connected space Formula: see text. This paper gives the cohomology classification of Formula: see text if the mod 2 or rational cohomology of the orbit space Formula: see text is isomorphic to the product of a projective space and sphere Formula: see text, where Formula: see text or Formula: see text, respectively. For a free involution on Formula: see text, a lower bound of covering dimension of the coincidence set of a continuous map Formula: see text is also determined.