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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Branched extensions of curves in compact surfaces

Author: Cloyd L. Ezell
Journal: Trans. Amer. Math. Soc. 259 (1980), 533-546
MSC: Primary 57M12; Secondary 30C15
MathSciNet review: 567095
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Abstract: A polymersion is a map $F: M \to N$ where M and N are compact surfaces, orientable or nonorientable, M a surface with boundary, where (a) At each interior point of M, there is an integer $n \geqslant 1$ such that F is topologically equivalent to the complex map ${z^n}$ in a neighborhood about the point. (b) At each point x in the boundary of M, $\delta M$, there is a neighborhood U containing x such that U is homeomorphic to F(U). A normal polymersion is one where $F(\delta M)$ is a normal set of curves in N. We are concerned with establishing a combinatorial representation for normal polymersions which map to arbitrary compact surfaces.

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Keywords: Polymersion, normal curve, assemblage, extension of a normal curve
Article copyright: © Copyright 1980 American Mathematical Society