Unoriented branched coverings arising from group actions

Young, Virginia R.

doi:10.1090/S0002-9939-1985-0774017-3

Unoriented branched coverings arising from group actions
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by Virginia R. Young

Proc. Amer. Math. Soc. 93 (1985), 525-531

DOI: https://doi.org/10.1090/S0002-9939-1985-0774017-3

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Abstract:

For an unbranched covering $f:{M^n} \to {N^n},[M] = (\deg f)[N]$ in unoriented cobordism ${\mathfrak {N}_*}$. Thus, in general, if $f:M \to N$ is a branched covering, then $[M] - (\deg f)[N]$ depends upon the branching behavior. In this note we describe the ideal ${I_G}$ of unoriented cobordism classes $[{M^n}] - |G|[{M^n}/G]$, where $G$ is a finite group acting on $M$ so that $M \to M/G$ is a $|G|$-fold smooth branched covering of closed smooth manifolds.

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