2026-06-28T15:33:20Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/507542023-08-28T08:18:48Zcom_20.500.14352_14col_20.500.14352_15

Branched coverings after Fox Montesinos Amilibia, José María General branched coverings, folded coverings, and branched folded coverings are all special cases of the spreads introduced by R. H. Fox in the 1950's [in A symposium in honor of S. Lefschetz, 243–257, Princeton Univ. Press, Princeton, N.J., 1957;] to put the point set topology of these objects on a solid footing. This largely expository article revisits the subject, giving it a full treatment. Certain definitions are extended and several essentially new sufficient conditions for a map to be a spread are given. The concept of a singular covering is introduced, allowing a common treatment of branched coverings and branched folded coverings. One motivation for re-examining and extending the theory is for applications to possibly wild knots. In addition, the theory contains, for example, the end compactification of Freudenthal as a special case, which is given a complete treatment here. The paper opens with a useful, detailed historical survey putting all the work in the area in a common framework. 2023-06-20T10:36:31Z 2023-06-20T10:36:31Z 2005 journal article 1405-213X https://hdl.handle.net/20.500.14352/50754 http://sociedadmatematicamexicana.org.mx/doc/pdf/11-1-4.pdf http://sociedadmatematicamexicana.org.mx/smm.php eng BMF-2002-04137-C02-01 restricted access Sociedad Matemática Mexicana