All three-manifolds are pullbacks of a branched covering to

Authors:
Hugh M. Hilden, María Teresa Lozano and José María Montesinos

Journal:
Trans. Amer. Math. Soc. **279** (1983), 729-735

MSC:
Primary 57N10

DOI:
https://doi.org/10.1090/S0002-9947-1983-0709580-4

MathSciNet review:
709580

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Abstract: There are two main results in this paper. First, we show that every closed orientable -manifold can be constructed by taking a pair of disjoint bounded orientable surfaces in , call them and ; taking three copies of ; splitting the first along , the second along and , and the third along ; and then pasting in the natural way. Second, we show that given any closed orientable -manifold there is a -fold irregular branched covering space, , such that is the pullback of the -fold irregular branched covering space branched over a pair of unknotted unlinked circles.

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0709580-4

Article copyright:
© Copyright 1983
American Mathematical Society