Decomposability problem on branched coverings

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Bedoya, Natalia A. Viana
Goncalves, Daciberg Lima
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Abstract
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Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected close surface N with Euler's characteristic less than or equal to 0. This shows that decomposable and indecomposable realizations may coexist. Moreover, we characterize the branch data of a decomposable primitive branched covering.
Comment: 19 pages. In this new version we improved the proofs and the presentation of the work.
Keywords
Mathematics - Geometric Topology, 57M12 (Primary), 20B35 (Secondary)
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