Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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

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
Torus/Z2
Posted: Jun 30, 2011 5:45 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

I can't find the answer to the following simple question:

In R^4 I have a torus T:

(x1)^2+(x2)^2=1
(x3)^2+(x4)^2=1

The group Z_2 acts on this torus via the reflection F(x)=-x, x=(x1,x2,x3,x4)

What kind of a surface do we get by taking the quotient T/Z_2? Again torus? Sphere? Klein bottle? Something else? What would be the answer and to get it?

Thanks

P.S. For the standard torus in R^3 and another action of Z_2 the answer is in an example in do Carmo book on differential geometry of surfaces.


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.