We prove that every closed connected orientable n-dimensional pseudomanifold, which is n-colored on its vertex set, is a covering of the n-sphere branched over the (n-2)-skeleton of an n-simplex. This extends a theorem of Alexander (Bull. Amer. Math. Soc. 26 (1920)) and a theorem of Ramirez (An. Inst. Mat. Univ. Nac. Autonoma Mexico 15 (1975)). Using the concept of contracted triangulation, every closed connected orientable 3-manifold M is represented as a covering of the 3-sphere branched over an universal graph G, so that the cardinality of the fiber of each point of G depends only on the number of the 3-simplexes of a contracted triangulation of M.

Contracted triangulations as branched coverings / Cavicchioli, Alberto; Grasselli, Luigi. - In: ATTI DEL SEMINARIO MATEMATICO E FISICO DELL'UNIVERSITA' DI MODENA. - ISSN 0041-8986. - STAMPA. - 33:(1984), pp. 241-246.

Contracted triangulations as branched coverings

CAVICCHIOLI, Alberto;GRASSELLI, Luigi
1984-01-01

Abstract

We prove that every closed connected orientable n-dimensional pseudomanifold, which is n-colored on its vertex set, is a covering of the n-sphere branched over the (n-2)-skeleton of an n-simplex. This extends a theorem of Alexander (Bull. Amer. Math. Soc. 26 (1920)) and a theorem of Ramirez (An. Inst. Mat. Univ. Nac. Autonoma Mexico 15 (1975)). Using the concept of contracted triangulation, every closed connected orientable 3-manifold M is represented as a covering of the 3-sphere branched over an universal graph G, so that the cardinality of the fiber of each point of G depends only on the number of the 3-simplexes of a contracted triangulation of M.
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Contracted triangulations as branched coverings / Cavicchioli, Alberto; Grasselli, Luigi. - In: ATTI DEL SEMINARIO MATEMATICO E FISICO DELL'UNIVERSITA' DI MODENA. - ISSN 0041-8986. - STAMPA. - 33:(1984), pp. 241-246.
Cavicchioli, Alberto; Grasselli, Luigi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/451025
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