The Jordan-Schönflies Theorem and the Classification of Surfaces

by Carsten Thomassen

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.