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The Jordan-Schoenflies 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<sub>3,3</sub> is non-planar. It then shows that the Jordan-Schoenflies 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-Schoenflies Theorem.
About the Author: Carsten Thomassen was at the Technical University of Denmark at the time of publication.