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STRUCTURE THEOREMS FOR RIEMANN AND TOPOLOGICAL SURFACES

Published online by Cambridge University Press:  28 January 2004

VENANCIO ÁLVAREZ  and
JOSÉ M. RODRÍGUEZ
VENANCIO ÁLVAREZ
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, [email protected]
JOSÉ M. RODRÍGUEZ
Affiliation:
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad, 30, 28911 Leganés, [email protected]
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Abstract

The classification theorem of compact surfaces states that every topological orientable compact surface is homeomorphic to a sphere or to a ‘torus’ of genus $g$, with $g\,=\,1,2,\dots$. It is proved in the paper that every hyperbolic Riemann surface except for $\bold D\setminus\{0\}$ can be decomposed into basic pieces of only a few different types: Y-pieces, funnels and half-disks. As a corollary of this result, the generalization of the classification theorem to non-compact surfaces is obtained.

Keywords

30F45
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 153 - 168
Copyright
The London Mathematical Society 2004

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