Lifting surgeries to branched covering spaces

Hilden, Hugh M.; Montesinos, José María

doi:10.1090/S0002-9947-1980-0561830-0

Lifting surgeries to branched covering spaces
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by Hugh M. Hilden and José María Montesinos PDF

Trans. Amer. Math. Soc. 259 (1980), 157-165 Request permission

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.

References

Allan L. Edmonds, Extending a branched covering over a handle, Pacific J. Math. 79 (1978), no. 2, 363–369. MR 531324
Israel Berstein and Allan L. Edmonds, On the construction of branched coverings of low-dimensional manifolds, Trans. Amer. Math. Soc. 247 (1979), 87–124. MR 517687, DOI 10.1090/S0002-9947-1979-0517687-9
Israel Berstein and Allan L. Edmonds, The degree and branch set of a branced covering, Invent. Math. 45 (1978), no. 3, 213–220. MR 474261, DOI 10.1007/BF01403169

Sobre la conjetura de Poincaré y los recubridores ramificados sobre un nudo

José M. Montesinos, Three-manifolds as $3$-fold branched covers of $S^{3}$, Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 85–94. MR 394630, DOI 10.1093/qmath/27.1.85
José María Montesinos, $4$-manifolds, $3$-fold covering spaces and ribbons, Trans. Amer. Math. Soc. 245 (1978), 453–467. MR 511423, DOI 10.1090/S0002-9947-1978-0511423-7