On the genus of smooth 4-manifolds

Cavicchioli, Alberto

doi:10.1090/S0002-9947-1992-1034659-5

On the genus of smooth $4$-manifolds
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by Alberto Cavicchioli

Trans. Amer. Math. Soc. 331 (1992), 203-214

DOI: https://doi.org/10.1090/S0002-9947-1992-1034659-5

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Abstract:

The projective complex plane and the "twisted" ${S^3}$ bundle over ${S^1}$ are proved to be the unique closed prime connected (smooth or $\text {PL}$) $4$-manifolds of genus two. Then the classification of the nonorientable $4$-manifolds of genus $4$ is given. Finally the genus of a manifold $M$ is shown to be related with the $2$nd Betti number of $M$ and some applications are proved in the general (resp. simply-connected) case.

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