Please keep in mind that this outline of what we shall talk about is very tentative and will likely change quite a bit as the drama of the semester unfolds. I.Identification Spaces

A. the identication, or quotient topology(section 4.2)
B. identification maps(section 4.2)

II.The Fundamental Group

A. homotopic maps(section 5.1)
B. the fundamental group(section 5.2)
C. examples(section 5.3)
D. homotopy type(section 5.4)
E. Jordan curve theorem(section 5.6)

III.Free Groups

IV.Triangulations

A. simplicial complexes(section 6.1)
B. simplicial approximation(sections 6.2 and 6.3
C. calculations(section 6.4)

V. Surfaces

A. symbols
B. classification
C. Euler characteristic and genus

VI.Simplicial Homology

A. cycles and boundaries(section 8.1)
B. homology groups(section 8.2)
C. examples(section 8.3)
D. simplicial maps(section 8.4)
E. invariance(sections 8.5 and 8.6)
F. Brouwer fixed point theorem (section 8.6)

28 December 2000