Linear actions of on

For an odd prime p , we consider free actions of (Z_/p)² on S²ⁿ⁻¹× S²ⁿ⁻¹ given by linear actions of (Z_/p)² on R⁴ⁿ . Simple examples include a lens space cross a lens space, but k -invariant calculations show that other quotients exist. Using the tools of Postnikov towers and surgery theory, the quotients are classified up to homotopy by the k -invariants and up to homeomorphism by the Pontrjagin classes. We will present these results and demonstrate how to calculate the k -invariants and the Pontrjagin classes from the rotation numbers.