Surface classification theorem

Lecturer: Guillermo Gallego

Date: 28/02/2018

Time: 17:00

Place: Room Alberto Dou (2nd floor, Faculty of Mathematics UCM)


It is a long known result that closed (compact, without boundary) topological surfaces can be classified according to their Euler’s characteristic and to their orientability. In this lecture we will see a (rather informal) elementary proof of this result, easily accessible to 1st year of degree students and virtually to anyone interested in the topic, as it involves just doing some (smart) drawings in the blackboard. The proof is based on the approach by John H. Conway, which he decided to call “The ZIP” (Zero Irrelevance Proof).


  • George K. Francis and Jeffrey R. Weeks. Conway’s ZIP Proof. Am. Math Monthly 106 (1999), 393-399. Online.

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