Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How can I explain the concept of a fiber bundle to someone with no mathematical background?

share|improve this question

2 Answers 2

up vote 6 down vote accepted

Draw a picture! For example you could use:

  • the cylinder for a (trivial) $S^1$-bundle over $\mathbb{R}$
  • the Möbius strip for a (non-trivial) $(0,1)$-bundle over $S^1$
  • the volume between two spheres of different radius for a (trivial) $(0,1)$-bundle over $S^2$
  • the torus for a (trivial) $S^1$-bundle over $S^1$

I think that those can already give some kind of intuition on what a fibre bundle is, in particular the Möbius strip is an easy non-trivial example. You can explain how it is different from the others by noticing that you cannot deform the Möbius strip into a cyilinder.

share|improve this answer
1  
Also, it would be helpful to talk about a Cartesian product. Some examples might be best made physical -- like all the configurations of an hour hand and a minute hand on a clock as a "physical" $S^1 \times S^1$. –  Ryan Budney Aug 13 '13 at 17:27

I would say draw an example of a space which can be exhibited as a fiber bundle, draw in the base space as a subspace (if this is possible) and then show that for a sufficiently small neighbourhood around a point in the base space, the fiber of the neighbourhood just looks like the product of the neighbourhood and the fiber. Some easy starting examples would be a compact product space (why not pick a square, cylinder and a torus - all easy to draw) to show that there are trivial bundles, and then something a bit more exotic like a Möbius strip or a covering space (the connected double cover of a circle seems like a good start).

The point is that examples are definitely the best way to get the point across.

share|improve this answer
    
I like the idea of the connected double cover of the circle, I never thought of it as a fibre bundle. –  Daniel Robert-Nicoud Aug 13 '13 at 17:19
1  
Covering spaces are really just fiber bundles with discrete fibers. –  Daniel Rust Aug 13 '13 at 17:20

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.