Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

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


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

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

Advanced Search
Reply to this Topic Reply to this Topic

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
6/30/11
Read Torus/Z2
Arkadiusz Jadczyk
7/1/11
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]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.