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Resumen:
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This paper establishes two new ways of representing all closed orientable 3-manifolds. (1) Let F,N be a pair of disjoint bounded orientable surfaces in the 3-sphere S3. Let (Sk,Fk,Nk), k=1,2,3, be 3 copies of the triplet (S,F,N). Split S1 along F1; S2 along F2 and N2; S3 along N3. Glue F1 to F2, N2 to N3 to obtain a closed orientable 3-manifold. Then every closed orientable 3-manifold can be obtained in this way. (2) Let q:S?S be any 3-fold irregular branched covering of the 3-sphere S over itself. Let M be any 3-manifold. Then there is a 3-fold irregular branched covering p:M?S and a smooth map f:S?S such that f is transverse to the branch set of q and p is the pullback of q and f.
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