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4-manifolds, 3-fold covering spaces and ribbons.

Montesinos Amilibia, José María (1978) 4-manifolds, 3-fold covering spaces and ribbons. Transactions of the American Mathematical Society, 245 . pp. 453-467. ISSN 0002-9947

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It is shown that a PL, orientable 4-manifold with no 3- or 4-handles is a 3-fold irregular cover of the 4-ball, branched over a ribbon 2-manifold. The author also studies 2-fold branched cyclic covers and finds examples of surfaces in S4 whose 2-fold branched covers are again S4; this gives new examples of exotic involutions on S4 [cf. C. McA. Gordon, Proc. London Math. Soc. (3) 29 (1974), 98–110]. The conjecture that any closed, orientable 4-manifold is an irregular 4-fold branched cover of S4 is reduced to studying bordism classes of irregular 4-fold covers of S3 with covering space equal to a connected sum of copies of S1×S2.

Item Type:Article
Uncontrolled Keywords:Covering spaces; Topological manifolds.
Subjects:Sciences > Mathematics > Topology
ID Code:17262

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Last Modified:07 Feb 2014 09:44

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