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Affine transverse foliations in sphere bundles
Let~$S^{n-1}\rightarrow E \rightarrow M^n$ be an oriented sphere bundle supporting a {smooth} affine transverse foliation. We give a new and elementary proof of the following fact: if the fundamental group {$π_1(M^n)$} is amenable, then the Euler number of the bundle vanishes. As a by-product, w
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