Lecture 6
Ch 1, Sec 8
Define the Euler characteristic. Compute the euler characteristics of all
of the compact surfaces. Deduce that the surfaces occuring in the
classification are all non-homeomorphic.
Ideas: why is the notion of Euler characteristic as presented in this
section unsatisfactory? Consider looking at exercise 8.1 (it's fun).
Do each of the steps 2-5 of the proof of Theorem 7.2 preserve the Euler
characteristic?