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Basically an exotic sphere is topologically a sphere, but doesn't look like a one. Or more accurately:

homeomorphic but not diffeomorphic to the standard Euclidean n-sphere

The first exotic spheres were constructed by John Milnor (1956) in dimension n = 7 as S3-bundles over S4.

It looks like an SU(2) gauge field on S4? But I don't know more about this? I guess there is lots of expertise here. Could you give a physical interpretation of this 7 sphere? Just to make it more intuitive.

http://en.wikipedia.org/wiki/Exotic_sphere

Thank you!

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Related: physics.stackexchange.com/q/879/2451 –  Qmechanic Nov 8 '12 at 6:37
    
@Qmechanic: Why is that question related? –  user1504 Nov 8 '12 at 20:00
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