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Proceedings of the American Mathematical Society

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Unoriented branched coverings arising from group actions


Author: Virginia R. Young
Journal: Proc. Amer. Math. Soc. 93 (1985), 525-531
MSC: Primary 57S17; Secondary 57R75
DOI: https://doi.org/10.1090/S0002-9939-1985-0774017-3
MathSciNet review: 774017
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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}] - \vert G\vert[{M^n}/G]$, where $ G$ is a finite group acting on $ M$ so that $ M \to M/G$ is a $ \vert G\vert$-fold smooth branched covering of closed smooth manifolds.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0774017-3
Article copyright: © Copyright 1985 American Mathematical Society

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