Geodesic
The structure of the set of singular points of piecewise-linear branched coverings of manifolds
Izvestiya. Mathematics , Tome 27 (1986) no. 3, pp. 549-573.

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The purpose of the paper is to provide a systematic account of the principles and methods of the theory of branched coverings in the piecewise-linear category. The regularity tests for branched coverings comprise the principal method of investigation presented in the paper. Bibliography: 31 titles. 
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I. V. Savel'ev. The structure of the set of singular points of piecewise-linear branched coverings of manifolds. Izvestiya. Mathematics , Tome 27 (1986) no. 3, pp. 549-573. http://geodesic.mathdoc.fr/item/IM2_1986_27_3_a6/

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