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The Jordan-Schönflies Theorem and the Classification of Surfaces

Year of Award: 1993

Publication Information: The American Mathematical Monthly, vol. 99, 1992, pp. 116-130

Summary: This paper contains a proof of the Jordan Curve Theorem based on the trivial result that \(K_{3,3}\) is non-planar.  It then shows that the Jordan-Schönflies Theorem forms a bridge between the Jordan Curve Theorem and the classification of compact surfaces, and presents a new graph-theoretic proof of the Jordan-Schönflies Theorem.

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About the Author: Carsten Thomassen was at the Technical University of Denmark at the time of publication.

 

Author (old format): 
Carsten Thomassen
Author(s): 
Carsten Thomassen
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Publication Date: 
Tuesday, September 23, 2008
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This paper contains a proof of the Jordan Curve Theorem based on the trivial result that \(K_{3,3}\) is non-planar. It then shows that the Jordan-Schönflies Theorem forms a bridge between the Jordan Curve Theorem and the classification of compact surfaces, and presents a new graph-theoretic proof of the Jordan-Schönflies Theorem.

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