Non-compact surface classification theorem

Lecturer: Mauro Sanchiz

Date: 14/03/2018

Time: 17:00

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


It’s common for degree students to receive some classes in their last years in which they enunciate and prove the Surface classification theorem for compact, boundaryless surfaces. They may even see the classification of compact surfaces with boundaries, which are classified according to their Euler’s characteristic, their orientability and number of boundary curves. In this lecture, we seek to go further and give a description of the non-compact surfaces and its classification theorem which is, surprisingly, not much harder than the previous theorems.

This lecture is intended as a continuation of the last lecture of Dedekind’s Army on the classification of compact surfaces, by Guillermo Gallego.


  • Mauro Sanchiz. Clasificación de superficies no compactas. Online.
  • I. Richards. On the Classification of Noncompact Surfaces. Online

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