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Math Forum » Discussions » Math Topics » geometry.research.independent

Topic: Torus/Z2
Replies: 1   Last Post: Jul 1, 2011 7:49 AM

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Arkadiusz Jadczyk

Posts: 2
From: France
Registered: 6/30/11
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.)
Date Subject Author
6/30/11
Read Torus/Z2
Arkadiusz Jadczyk
7/1/11
Read Re: Torus/Z2
Arkadiusz Jadczyk

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