Date: Jul 1, 2011 7:49 AM
Author: Arkadiusz Jadczyk
Subject: Re: Torus/Z2

Thanks to all who replied privately. It it the Clifford torus again. Can be seen for instance by considering the map

(z1,z2)->(z1 z2, z1 bar(z2))

where z1,z2 are complex numbers with |z1|=|z2|=1, and bar denotes complex conjugate. This maps Clifford torus onto Clifford torus (surjection) and is constant on the orbits of Z_2 acting by (z1,z2)->(-z1,-z2).

Of course the result can be obtained by indirect, more refined mathematical methods (Euler characteristic etc.)