Affine transverse foliations in sphere bundles

2026/03/01 by Ilya Alekseev, Ivan Nasonov, Gaiane Panina
Mathematics · #math.GT

paper · pdf

Abstract

Let~S^n-1→ E → Mⁿ be an oriented sphere bundle supporting a smooth affine transverse foliation. We give an upper bound for the Euler number of the bundle. We also give a new and elementary proof of the following fact: if the fundamental group π₁(Mⁿ) is amenable, then the Euler number of the bundle vanishes.

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