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

The only genus zero 𝑛-manifold is 𝑆ⁿ