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Is it known whether, for any fibration of a sphere with connected fibres, the fibre has to be a sphere? S^1$S^1$, S^3$S^3$ or S^7$S^7$?

Is it known whether, for any fibration of a sphere with connected fibres, the fibre has to be a sphere? S^1, S^3 or S^7?

Is it known whether, for any fibration of a sphere with connected fibres, the fibre has to be a sphere? $S^1$, $S^3$ or $S^7$?

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Terry Wall
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Is any connected fibre of a fibration of a sphere also a sphere?

Is it known whether, for any fibration of a sphere with connected fibres, the fibre has to be a sphere? S^1, S^3 or S^7?