Maths Video:Visible Fibre Bundle

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In summary, the conversation is about a maths seminar video discussing the concept of fibre bundles in modern differential geometry. The speaker mentions that their English is poor but they find the video to be helpful and interesting. They also ask for advice on how to embed the video and receive suggestions for improving the quality, such as using a tripod, microphone, and better lighting. The conversation ends with a suggestion to film in a different location for better results.
  • #1
Strongart
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Here is my maths seminar video:Visible Fibre Bundle,discussing the vivid picture of fibre bundle which is the basic concept in the modern differential geometry.
My English is poor,but I think the maths ideal is helpful and interesting.

[flash]http://www.tudou.com/v/-HUCJSHLdWU/&rpid=6075939&resourceId=6075939_04_05_99/v.swf[flash]

How to embed it?
 
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  • #2
I didn't have time to watch enough to comment on the mathematics, but I have one huge suggestion for you: talk to someone who knows a lot about making videos! If you don't know anyone, then here are a few things I will suggest (someone who knows more about it can probably give you more and better ideas than these):
  1. Use a tripod. The low camera angle is distracting.
  2. Use a microphone. We can barely hear you.
  3. Clean that whiteboard, find a way to mount it on the wall, and temporarily get rid of that thing hanging above it. All this stuff is distracting.
  4. More light! Sometimes you are just a shadow against the whiteboard. The more diffuse the better, so you don't cast distracting shadows.

The second two points might be more easily addressed by filming in a different location.
 

1. What is a visible fibre bundle in mathematics?

A visible fibre bundle is a mathematical concept used to study the topological properties of a space. It consists of a continuous projection map between two topological spaces, where the base space is a manifold and the fibre space is a topological space. The projection map must preserve certain properties, such as continuity and local homeomorphism, in order for it to be considered a fibre bundle.

2. How is a visible fibre bundle different from a regular fibre bundle?

While a regular fibre bundle only requires the projection map to be continuous and locally homeomorphic, a visible fibre bundle has the additional requirement that the projection map must preserve the visibility of the fibres. This means that the projection map must be injective, meaning that each point in the base space must map to a unique point in the fibre space.

3. What are some applications of visible fibre bundles in mathematics?

Visible fibre bundles have many applications in mathematics, including in topology, differential geometry, and physics. They are useful for studying the structure of manifolds, understanding the behavior of vector fields, and modeling physical systems such as electromagnetic fields.

4. How are visible fibre bundles represented visually?

Visible fibre bundles can be represented visually in various ways, depending on the specific context. In general, they are often depicted as a base space with fibres attached to each point, with the projection map showing how the fibres are mapped to the base space. In differential geometry, they are often represented as a tangent bundle, where the base space is a manifold and the fibres are tangent spaces at each point.

5. What are some key properties of visible fibre bundles?

Some key properties of visible fibre bundles include the local triviality property, which states that the projection map must be locally equivalent to the projection onto the base space, and the homotopy invariance property, which states that the topological properties of the base space are preserved under homotopy. Additionally, visible fibre bundles can be classified using the concept of a characteristic class, which assigns a unique class to each bundle based on its topological properties.

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