Problem set  Due date  Problems  Solutions (outline) 
1 
September 4 
Chapter 0: 4, 5, 6, 9, 13 Section 1.1: 6, 7, 16 (a,b,c,f), 20. (Remark: for 1.1 #20, I don't think you really need to use Lemma 1.19.) 
HW 1 
2 
September 11 
Section 1.2: 1, 4, 6, 8, 9, 11. 
HW 2 
3 
September 18 
Section 1.2: 12, 14, 22. Extra problem: Use the Wirtinger presentation to calculate the fundamental group of the complement of the trefoil knot. (See here for a picture of the trefoil.) If all goes well, we'll see in class another way to calculate this fundamental group, resulting in the group with generators x, y and relation x^{2}=y^{3}. Prove that your answer algebraically agrees with this group by finding an explicit isomorphism between the two groups. 
HW 3 
4 
September 25 
Section 1.3: 4, 5, 7, 8. For #8, there's a typo: "Exercise 10 in Chapter 0" should be "Exercise 11 in Chapter 0." If you do use Exercise 11, please provide a proof. 
HW 4 
5 
October 2 
Section 1.3: 10, 11, 14. To clarify: in #14, "Find all the connected covering spaces" is in the same sense as #10. 
HW 5 
6 
October 16 
Section 1.3: 16, 18, 19, 20. For #19, please disregard the final sentence. (You can certainly think about it if you like, but I think it could use some clarification and I've decided it isn't worth it.) 
HW 6

7 
October 23 
Section 2.1: 2, 4, 5, 7, 8. 
HW 7

8 
November 6 
Section 2.1: 14, 15, 16, 17, 26. For this problem set, please note that you can assume that simplicial and singular homology are isomorphic. For #26, you may want to follow the idea of Example 1.25 to prove that relative H_{1} of X/A is uncountable. (Don't just cite Example 1.25, although you can adapt its argument  your argument should involve H_{1} rather than the fundamental group.) 
HW 8 
9 
November 13 
Section 2.1: 20, 22, 27. (For #20, see pp. 89 for the definitions of suspension and cone. Also, after you've solved #20, please think about #21 but you don't need to turn it in.) For these problems, you can use anything in section 2.1. (In particular, you can use the Five Lemma on p. 129; I'll get to this soon in class, but feel free to use it in the meantime.) 
HW 9 
10 
November 20 
HW 10 
HW 10 
11 
December 4 
Note: please do these problems but don't turn them in. I've posted solutions (to the right). Section 2.2: 2, 3, 11, 12, 14, 20, 22, 23. 
HW 11 
Takehome final
exam is due on Friday December 13 at noon. 

Hatcher Algebraic Topology: link to online version of the textbook
Course lecture notes part 1
Course lecture notes part 2
Note!: Don't treat
these notes as a definitive reference; they certainly contain
mistakes and may not correspond precisely to what we actually cover in
class.