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 2nd Betti number of M and some applications are proved in the general (resp. simply-connected) case.
On the genus of smooth 4-manifolds / Cavicchioli, Alberto. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 331 (1):(1992), pp. 203-214.
On the genus of smooth 4-manifolds
CAVICCHIOLI, Alberto
1992
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 2nd Betti number of M and some applications are proved in the general (resp. simply-connected) case.
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