We continue the topological classification of closed connected orientable 4-manifolds according to the (regular) genus. In particular, we prove that any closed prime orientable PL 4-manifold of genus six is topologically homeomorphic to a lens-fiber bundle over the 1-sphere. There are good reasons to conjecture that the genus six characterizes the topological product RP^3 X S^1 of the real projective 3-space by the 1-sphere among closed connected prime orientable 4-manifolds.
On the genus of RP^3 X S^1 / Spaggiari, Fulvia. - In: COLLECTANEA MATHEMATICA. - ISSN 0010-0757. - STAMPA. - 50:(1999), pp. 229-241.
On the genus of RP^3 X S^1
SPAGGIARI, Fulvia
1999
Abstract
We continue the topological classification of closed connected orientable 4-manifolds according to the (regular) genus. In particular, we prove that any closed prime orientable PL 4-manifold of genus six is topologically homeomorphic to a lens-fiber bundle over the 1-sphere. There are good reasons to conjecture that the genus six characterizes the topological product RP^3 X S^1 of the real projective 3-space by the 1-sphere among closed connected prime orientable 4-manifolds.
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