Lecture 3

Massey: Ch. 1, Sec. 5.

State the classification theorem of compact surfaces - our short-term goal is to prove this thing.

Ideas: explain the cannonical forms for our surfaces. Why do these give use the surfaces we think they do? How is connect sum showing up in the polygons representation? How do we recognize orientablity in these. Do many examples - what does a three holed torus connect sum a projective space look like in polygonal representation? Why are these things compact surfaces?