| Título: | Lifting surgeries to branched covering spaces |
| Autores: | Montesinos Amilibia, José María ; Hilden, Hugh Michael |
| Tipo de documento: | texto impreso |
| Editorial: | American Mathematical Society, 1980 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/restrictedAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Topología , Tipo = Artículo |
| Resumen: |
Long ago J. W. Alexander showed that any closed, orientable, triangulated n-manifold can be expressed as a branched covering of the n-sphere [Bull. Amer. Math. Soc. 26 (1919/20), 370–372; Jbuch 47, 529]. In general, the branch set is not a manifold and no useful information is given about the degree of the branched covering. When n=3, however, he did indicate that the branch set could be arranged to be a link. Much more recently, the first author [Amer. J. Math. 98 (1976), no. 4, 989–997], U. Hirsch [Math. Z. 140 (1974), 203–230] and the second author [Quart. J. Math. Ser. (2) 27 (1976), no. 105, 85–94] showed that when n=3 the branched covering can be constructed to have degree 3 and a knot as branch set. Of course, these branched coverings are highly irregular. The authors here address similar questions in higher dimensions. Starting with a branched covering Mn?Sn, the authors give some technical, sufficient conditions for a manifold obtained from Mn by a single surgery to be a branched covering of Sn of the same degree and with a branch set easily described in terms of the initial branch set. The nicest corollary of the general technique is that if Mn?Sn is a branched covering of degree d, then there is a branched covering Mn×Sk?Sn+k of degree d+1. The new branch set is an orientable and/or locally flat submanifold if and only if the original branch set is. In particular, the n-torus is an n-fold branched covering of the n-sphere, branched along a locally flat, orientable submanifold. (For known cohomological reasons, n is the smallest possible degree of such a branched covering.) |
| En línea: | https://eprints.ucm.es/id/eprint/17224/1/Montesinos20.pdf |
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