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

 

A combinatorial characterization of $ S\sp 3\times S\sp 1$ among closed $ 4$-manifolds


Author: Alberto Cavicchioli
Journal: Proc. Amer. Math. Soc. 105 (1989), 1008-1014
MSC: Primary 57N13; Secondary 57M15, 57Q05, 57Q15
MathSciNet review: 931726
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Abstract: The topological product $ {S^3} \times {S^1}$ is proved to be the unique closed connected $ 4$-manifold of regular genus one. As a consequence, the complex projective plane $ C{P^2}$ has regular genus two.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0931726-4
PII: S 0002-9939(1989)0931726-4
Keywords: PL-manifold, contracted triangulation, pseudocomplex, multigraph, edge-coloured graph, $ 2$-cell imbedding, crystallization, regular genus
Article copyright: © Copyright 1989 American Mathematical Society