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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Maps between surfaces


Author: Richard Skora
Journal: Trans. Amer. Math. Soc. 291 (1985), 669-679
MSC: Primary 57M12; Secondary 57N05
MathSciNet review: 800257
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Abstract: The Uniqueness Conjecture states if $ \phi ,\,\psi :\,M \to N$ are $ d$-fold, simple, primitive, branched coverings between closed, connected surfaces, then $ \phi$ and $ \psi$ are equivalent. The Uniqueness Conjecture is proved in the case that $ M$ and $ N$ are nonorientable and $ N = \mathbf{R}{P^2}$ or Klein bottle. It is also proved in the case that $ M$ and $ N$ are nonorientable and $ d/2 < d\chi (N) - \chi (M)$. As an application it is shown that two $ d$-fold, branched coverings $ \phi :{M_1} \to N,\,\psi :{M_2} \to N$ between closed, connected surfaces are branched cobordant.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0800257-5
PII: S 0002-9947(1985)0800257-5
Keywords: Branched covering, Uniqueness Conjecture, branched cobordant
Article copyright: © Copyright 1985 American Mathematical Society