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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The only genus zero $ n$-manifold is $ S\sp{n}$


Authors: Massimo Ferri and Carlo Gagliardi
Journal: Proc. Amer. Math. Soc. 85 (1982), 638-642
MSC: Primary 57N15; Secondary 05C10, 05C15, 57Q15, 57Q99
MathSciNet review: 660620
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660620-5
PII: S 0002-9939(1982)0660620-5
Keywords: $ {\text{PL}}$-manifold, genus, Heegaard genus, multigraph, $ 2$-cell imbedding, regular genus, crystallization, pseudocomplex, generalized Poincaré Conjecture
Article copyright: © Copyright 1982 American Mathematical Society