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Construction of universal branched coverings

✍ Scribed by Neal Brand; Débora María Tejada

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
883 KB
Volume
76
Category
Article
ISSN
0166-8641

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✦ Synopsis

A construction for the classifying spaces for branched coverings with branch set a codimension 2 submanifold is given by Brand (1978Brand ( , 1980)). Using this result as a first step we inductively construct universal branched coverings with branch set a stratified set. We also give some of the lower homotopy groups of the classifying spaces which correspond to branched coverings of spheres.

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A well-known theorem of Alexander [1] says that every orientable surface is a branched covering of the sphere N2, and every nonorientable surface is a branched covering of the projective plane. In the study of surface branched coverings [2,3, 14], we can ask naturally as a generalization of Alexande