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Composites of open maps. (English. Russian original) Zbl 1035.57002

Sb. Math. 193, No. 3, 311-327 (2002); translation from Mat. Sb. 193, No. 3, 3-20 (2002).
The problem of representation of an open map as a composite of nontrivial open maps is investigated. In particular, the decomposition problem for coverings, regular and of general type, is considered. Simultaneously, necessary and sufficient conditions for a group to be not simple or solvable are obtained in terms of covering groups.
The authors give examples of coverings which are not compositions of nontrivial open maps. In particular, it is proved that there exists a nondecomposable 4-sheeted covering \(f:S_5\to S_2\) (Corollary 3.3). Here \(S_g\) is an orientable surface of genus \(g\).
It is shown that factorizability of branched data is an obstruction for decomposability of branched coverings.

MSC:

57M10 Covering spaces and low-dimensional topology
57M12 Low-dimensional topology of special (e.g., branched) coverings
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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