Möbius bundle

  • Thread starter seydunas
  • Start date
  • #1
39
0

Main Question or Discussion Point

Hi,

i can not understand how circle has a nontrivial bundle, Möbius bundle. Can you say me what is its transition function on it.
 

Answers and Replies

  • #2
lavinia
Science Advisor
Gold Member
3,165
575
Hi,

i can not understand how circle has a nontrivial bundle, Möbius bundle. Can you say me what is its transition function on it.
multiplication by -1.

Similarly the Klein bottle is reflection of a circle.

A way to visualize the Klein bottle is to look at the transformation (x,y) -> ( x+ 1/2,-y) on the unit square viewed as the fundamental domain of the torus.
 

Related Threads on Möbius bundle

Replies
2
Views
3K
  • Last Post
Replies
1
Views
767
  • Last Post
Replies
11
Views
3K
Replies
14
Views
7K
Replies
0
Views
3K
  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
1K
Top