Montesinos Amilibia, José MaríaHilden, Hugh MichaelLozano Imízcoz, María Teresa2023-06-212023-06-211983-101088-685010.2307/1999564https://hdl.handle.net/20.500.14352/64702This 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.engjournal articlehttp://www.jstor.org/stable/1999564http://www.jstor.org/restricted access515.16closed orientable 3-manifoldbranched coveringlinkknotTopología1210 Topología