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Re: Torus/Z2
Posted:
Jul 1, 2011 7:49 AM
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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.)
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