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2-sphere bundles over compact surfaces

2-sphere bundles over compact surfaces

Closed <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="4"> <mml:semantics> <mml:mn>4</mml:mn> <mml:annotation encoding="application/x-tex">4</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-manifolds which fiber over a compact surface with fiber a sphere are classified, and the fibration is shown to be unique (up to diffeomorphism).