The only genus zero 𝑛-manifold is 𝑆ⁿ

Ferri, Massimo; Gagliardi, Carlo

doi:10.1090/S0002-9939-1982-0660620-5

The only genus zero $n$-manifold is $S^{n}$
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by Massimo Ferri and Carlo Gagliardi PDF

Proc. Amer. Math. Soc. 85 (1982), 638-642 Request permission

Abstract:

All $n$-manifolds of regular genus zero, i.e. admitting a crystallization which regularly imbeds into ${{\mathbf {S}}^2}$, are proved to be homeomorphic to ${{\mathbf {S}}^n}$. A conjecture implying the Poincaré Conjecture in dimension four is also formulated. Si dimostra che tutte le $n$-varietà di genere regolare zero, cioè aventi una cristallizzazione che si immerge regularmente in ${{\mathbf {S}}^2}$, sono omeomorfe a ${{\mathbf {S}}^n}$. Si formula anche una congettura che implica quella di Poincaré in dimensione quattro.

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Graphs, groups and surfaces