Swan Homeomorphisms

Two object are called homeomorphic if they can be bi-continuosly deformed into each other. Here two swans are defromed together with their mirrorimages. The result is a torus for one swan and the union of two tori for the other. It is a deep topological theorem that these two can not be bi-continuously deformed into each other.

Remark: The by-continuous deformation in this clip only starts after the one swan has put its beak under its feathers. Touching parts of a space that did not touch is NOT a bi-continuous deformation.

This video was produced for a topology course at the Leibniz Universitat Hannover.

Category:

Howto & Style

Tags:

• topology
• swan
• homeomorphism
• bothmer

[0x7F800000]

What artistic freedom...? Deforming a Sphere into a genus 2 surface shows exacty what a homeomorphism is _not_.

[bothmer]

@0x7F800000: You are completely right. The swan should have bitten into his shoulder before the homeomorphism started.

[sMcLouder]

I believe the second swan is cheating. It should become a sphere, instead.

[bothmer]

You are right... (Maybe call it artistic feedom...)

[ihmc3jn09hk]

please clear the idea of topology involved with geometry@.@

[MiniMario6499]

0:50 8O

LOL

[volt800]

shit

[PrestigeProductionz]

FAKE!

[rasmusfribble]

Those conniving swans!

[sMcLouder]

Ah, artistic freedom is a good thing. Glad to hear that not all my math education washed off yet! ;-)