Year: 2026
Type: preprint
Abstract: 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, we give an upper bound for the Euler number of the bundle in the general case, that is, for non-amenable {$π_1(M^n)$}.
Source: arXiv (Cornell University)
Authors: Alekseev, Ilya, Nasonov, Ivan, Panina, Gaiane
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7133358932
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