The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics » geometry.research

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Arkadiusz Jadczyk

Posts: 2
From: France
Registered: 6/30/11
Re: Torus/Z2
Posted: Jul 1, 2011 7:49 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
Read Torus/Z2
Arkadiusz Jadczyk
Read Re: Torus/Z2
Arkadiusz Jadczyk

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.