RT Journal Article
T1 All three-manifolds are pullbacks of a branched covering S3 to S3
A1 Montesinos Amilibia, José María
A1 Hilden, Hugh Michael
A1 Lozano Imízcoz, María Teresa
AB 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.
PB American Mathematical Society
SN 1088-6850
YR 1983
FD 1983-10
LK https://hdl.handle.net/20.500.14352/64702
UL https://hdl.handle.net/20.500.14352/64702
LA eng
NO J. S. Birman and J. Powell, Special representation for 3-manifolds, Geometric Topology (J. C. Cantrell, ed.), Academic Press, 1979. H. M. Hilden, Embeddings and branched covering spaces for three and four dimensional manifolds, Pacific J. Math. 78 (1978), 139-147. H. M. Hilden and J. M. Montesinos, A method of constructing 3-manifolds and its application to the computation of the μ-invariant, Proc. Sympos. Pure Math., vol. 32, Part 2, Amer. Math. Soc., Providence, R.I., 1978, pp. 61-69.  R. Kirby, Problems in low dimensional manifold theory, Proc. Sympos. Pure Math., vol. 32, Amer. Math. Soc., Providence, R. I., 1978, pp. 273-312. J. M. Montesinos, A note on 3-fold branched coverings of S3, Math. Proc. Cambridge Philos. Soc. 88 (1980), 321-325.
NO Comisión Asesora del ME
DS Docta Complutense
RD 2 may 2024