Let X = RP(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}x RP^{n}

I know the following:

- the universal cover of X is Y = S^{n}x S^{n}

- 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 S^{2}x RP^{2}. 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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# Covering spaces of RP^n x RP^n

Can you offer guidance or do you also need help?

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