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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 638-642
  • MSC: Primary 57N15; Secondary 05C10, 05C15, 57Q15, 57Q99
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0660620-5
  • MathSciNet review: 660620