In this note we give a short and elementary proof of more general version Whitney’s theorem that 3-connected planar graphs have unique embedding in the plane. A consequence is also cubic plane cannot be embedded higher genus with simple dual. The aim paper to promote proof, which especially well suited for lectures presenting theorem.

This course will explain the fundamental concepts of topology for smooth manifolds. After developing the fundamental tool of transversality theory (we prove Sard’s theorem) we will prove the Brouwer Fixed Point Theorem, the Brouwer No Retraction Theorem, and the Whitney Embedding Theorem, and the “27 lines on a cubic surface” using this tool. Then we cover Morse Theory and use it to classify 2-...