Branched coverings. I

Stong, R. E.

doi:10.1090/S0002-9947-1983-0684516-3

Branched coverings. I
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Trans. Amer. Math. Soc. 276 (1983), 375-402 Request permission

Abstract:

This paper analyzes the possible cobordism classes $[M] - (\deg \;\phi )[N]$ for $\phi : M \to N$ a smooth branched covering of closed smooth manifolds. It is assumed that the branch set is a codimension $2$ submanifold. The results are a fairly complete description in the unoriented case, a partial description in the oriented case, and a detailed analysis of the case in which $N$ is a sphere.

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