1/18  Overview; Cell complexes  P. 18 

1/20  The fundamental
group  P. 2128  Homework 1, due Thursday 1/27

1/25  Fundamental group of the circle  P. 2931 

1/27  Brouwer & BorsukUlam theorems  P. 3134 

2/1  Induced homomorphisms  P. 3437  P. 3839, #8, 9, 10,
16. Due Tuesday 2/8

2/3  Van Kampen's theorem  P. 4046 

2/8  Applications of van
Kampen  P. 4652; extra
page 

2/10  Fundamental groups of
manifolds  Conway's
ZIP
Proof, Mapping
class group  Homework 3, due Thursday 2/17

2/15  Intro to covering spaces  P. 5661 

2/17  The universal
cover  P. 6365  Homework 4, due Thursday 2/24

2/22  Group actions  P. 7074 

2/24  Classification of covering spaces  P. 6162, 6668. 
Homework 5, due Tuesday 3/15.

3/1  Intro to homology  P. 97101. 

3/3  Simplicial homology  P. 102107. 

3/15  Singular homology: definitions  P. 108110.  P. 131132 #4, 5, 8,
10, 11. Due Thursday 3/24

3/17  Properties of singular homology  P. 110113. 

3/22  Exact sequences,
H_{1} vs. π_{1}  P. 113114, 166168. 

3/24  Long exact sequence of a pair  P. 114117.  P. 123
#14, 16, 17. P. 53 #9 (easier using homology!) Due 3/31

3/29  Excision (in a nutshell)  P. 117124 

3/31  Simplicial = singular homology  P. 125130 

4/5  Orientations, π_{1}, and homology  Lee,
p. 329334  Homework 8, due 4/14

4/7  Degrees of maps  P. 134135 

4/12  Degrees from smooth
theory  P. 136,
Wikipedia 

4/14  MayerVietoris
sequence  P. 149153  Homework 9, due 4/21

4/19  Intro to cohomology  P. 186189. 

4/21  De Rham cohomology  Lee, p. 388399 (skipping a lot). 

4/26  The de Rham theorem  Lee,
p. 425430.  Homework 10, due 5/5

4/28  Poincaré duality  P. 241248; Lee, p. 432; Wikipedia 
