Covering spaces of RP^n x RP^n

  • Thread starter mrbohn1
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Let X = RPn x RPn

I know the following:

- the universal cover of X is Y = Sn x Sn
- the fundamental group of X is G = Z/2Z x Z/2Z = {(0,0), (0,1), (1,0), (1,1)}
- Covering spaces of X are defined by actions of subgroups of G on Y

Each of the elements of G generates a subgroup of order two. Clearly the covering spaces defined by the action of <(0,1)> and <(1,0)> on Y are S2 x RP2. But what about the action of <(1,1)>? What covering space does this define?

And finally, which of the covering spaces are equivalent? And which are homeomorphic? Thanks.
 

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