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


Branched extensions of curves in orientable surfaces

Authors: Cloyd L. Ezell and Morris L. Marx
Journal: Trans. Amer. Math. Soc. 259 (1980), 515-532
MSC: Primary 57M12; Secondary 30C15
MathSciNet review: 567094
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Abstract: Given a set of regular curves $ {f_1}\,,\,\ldots,\,{f_\rho }$ in an orientable surface N, we are concerned with the existence and structure of all sense-preserving maps $ F:\,M\, \to \,N$ where

(a) M is a bordered orientable surface with $ \rho $ boundary components $ {K_1},\ldots,\,{K_\rho }$,

(b) $ F\vert{K_i}\, = \,{f_i},\,i\, = \,1,\,\ldots,\,\rho $,

(c) at each interior point of M, there is an integer n such that F is locally topologically equivalent to the complex map $ w\, = \,{z^n}$.

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PII: S 0002-9947(1980)0567094-6
Article copyright: © Copyright 1980 American Mathematical Society