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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Lifting surgeries to branched covering spaces

Authors: Hugh M. Hilden and José María Montesinos
Journal: Trans. Amer. Math. Soc. 259 (1980), 157-165
MSC: Primary 57M12; Secondary 57Q99
MathSciNet review: 561830
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Abstract: It is proved that if $ {M^n}$ is a branched covering of a sphere, branched over a manifold, so is $ {M^n}\, \times \,{S^m}$, but the number of sheets is one more. In particular, the n-dimensional torus is an n-fold simple covering of $ {S^n}$ branched over an orientable manifold. The proof involves the development of a new technique to perform equivariant handle addition. Other consequences of this technique are given.

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Keywords: n-manifolds, n-fold simple branched covering spaces, knots, equivariant surgery, moves
Article copyright: © Copyright 1980 American Mathematical Society