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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

All three-manifolds are pullbacks of a branched covering $ S\sp{3}$ to $ S\sp{3}$


Authors: Hugh M. Hilden, María Teresa Lozano and José María Montesinos
Journal: Trans. Amer. Math. Soc. 279 (1983), 729-735
MSC: Primary 57N10
MathSciNet review: 709580
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Abstract: There are two main results in this paper. First, we show that every closed orientable $ 3$-manifold can be constructed by taking a pair of disjoint bounded orientable surfaces in $ {S^3}$, call them $ {F_1}$ and $ {F_2}$; taking three copies of $ {S^3}$; splitting the first along $ {F_1}$, the second along $ {F_1}$ and $ {F_2}$, and the third along $ {F_2}$; and then pasting in the natural way. Second, we show that given any closed orientable $ 3$-manifold $ {M^3}$ there is a $ 3$-fold irregular branched covering space, $ p:{M^3} \to {S^3}$, such that $ p:{M^3} \to {S^3}$ is the pullback of the $ 3$-fold irregular branched covering space $ q:{S^3} \to {S^3}$ branched over a pair of unknotted unlinked circles.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0709580-4
PII: S 0002-9947(1983)0709580-4
Article copyright: © Copyright 1983 American Mathematical Society