Decomposability problem on branched coverings

Details Decomposability problem on branched coverings Decomposability problem on branched coverings

2007-07-19

arxiv.org/abs/0707.2949v4

Mathematics

Geometric Topology

19 pages. In this new version we improved the proofs and the presentation of the work.

Scientific paper

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.

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