All closed PL n-manifolds of regular genus zero, i.e. admitting a crystallization which regularly imbeds in S^2, are proved to be PL homeomorphic to S^n. A conjecture, implying the Poincarè conjecture in dimension four, is also formulated.
The only genus zero n-manifold is S^n / M., Ferri; Gagliardi, Carlo. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 85:(1982), pp. 638-642. [10.1090/S0002-9939-1982-0660620-3]
The only genus zero n-manifold is S^n
GAGLIARDI, Carlo
1982
Abstract
All closed PL n-manifolds of regular genus zero, i.e. admitting a crystallization which regularly imbeds in S^2, are proved to be PL homeomorphic to S^n. A conjecture, implying the Poincarè conjecture in dimension four, is also formulated.
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