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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
DOI: https://doi.org/10.1090/S0002-9947-1985-0800257-5
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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Keywords: Branched covering, Uniqueness Conjecture, branched cobordant
Article copyright: © Copyright 1985 American Mathematical Society