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Can anyone give me an explicit isomorphism between $SU(2)$ and the three sphere?

What about for higher spheres? This question link text seems to indicate that there exists an isomorphism a homeomorphism from $SU(n)/SU(n-1)$ to the $(2n-1)$-sphere.

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Can anyone give me an explicit isomorphism between $SU(2)$ and the three sphere?

What about for higher spheres? This question link text seems to indicate that there exists an isomorphism from $SU(n)/SU(n-1)$ to the $(2n-1)$-sphere.

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