2026-06-29T02:33:52Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/586562023-08-26T18:21:00Zcom_20.500.14352_14col_20.500.14352_15

Representing open 3-manifolds as 3-fold branched coverings Montesinos Amilibia, José María 515.162 3-manifolds Topología 1210 Topología It is a celebrated result of H. Hilden and the author of the present paper that every closed, connected, oriented 3-manifold is a 3-fold irregular (dihedral) branched covering of the 3-sphere, branched over a knot. Here the author explores a generalization of this result to the case of non-compact manifolds. It is shown that a non-compact, connected, oriented 3-manifold is a 3-fold irregular branched covering of an open subspace of S3, branched over a locally finite family of proper arcs. The branched covering is constructed in such a way that it extends to a branched covering (suitably understood) of the Freudenthal end compactification over the entire 3-sphere. In particular all (uncountably many) contractible open 3-manifolds may be expressed as 3-fold branched coverings of R3, branched over a locally finite collection of proper arcs. Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T18:48:05Z 2023-06-20T18:48:05Z 2002 journal article https://hdl.handle.net/20.500.14352/58656 1139-1138 eng restricted access application/pdf Springer