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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the genus of smooth $ 4$-manifolds


Author: Alberto Cavicchioli
Journal: Trans. Amer. Math. Soc. 331 (1992), 203-214
MSC: Primary 57N13; Secondary 57Q05, 57R60
DOI: https://doi.org/10.1090/S0002-9947-1992-1034659-5
MathSciNet review: 1034659
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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 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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DOI: https://doi.org/10.1090/S0002-9947-1992-1034659-5
Keywords: Smooth $ 4$-manifold, crystallization, genus, collapsing, intersection form, homotopy sphere
Article copyright: © Copyright 1992 American Mathematical Society

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