A combinatorial characterization of 𝑆³×𝑆¹ among closed 4-manifolds

Cavicchioli, Alberto

doi:10.1090/S0002-9939-1989-0931726-4

A combinatorial characterization of $S^ 3\times S^ 1$ among closed $4$-manifolds
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by Alberto Cavicchioli PDF

Proc. Amer. Math. Soc. 105 (1989), 1008-1014 Request permission

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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Graphs, groups and surfaces