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Branched coverings after Fox

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Montesinos Amilibia, José María (2005) Branched coverings after Fox. Boletín de la Sociedad Matemática Mexicana. Tercera Serie, 11 (1). pp. 19-64. ISSN 1405-213X

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Official URL: http://sociedadmatematicamexicana.org.mx/doc/pdf/11-1-4.pdf




Abstract

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.


Item Type:Article
Uncontrolled Keywords:spread, branched covering, folded covering.
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:22299
Deposited On:12 Jul 2013 12:53
Last Modified:12 Dec 2018 15:13

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