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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 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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0567095-8
PII: S 0002-9947(1980)0567095-8
Keywords: Polymersion, normal curve, assemblage, extension of a normal curve
Article copyright: © Copyright 1980 American Mathematical Society