Math 671 Problems

Problems are taken from Lee, Introduction to Topological Manifolds, 2nd ed. unless indicated otherwise. Exercises, denoted with an E, appear in-line in the chapter text and use a period for punctuation. Problems, denoted with a P, appear at the end of each chapter and use a hyphen for punctuation. Thus E2.2 appears on p.21 immediately after Example 2.1. P2–1 is the first problem of Chapter 2, which appears on p.45. Problems from Hatcher appear at the end of Chapter 0 and at the end of subsections within other chapters.

Submitting your work

HW should be put in the designated folder in my mailbox in the Math & Stat Mailroom on the 16th floor of LGRT. The HW will be collected by the grader on Friday in the morning. As long as your HW is in the folder before then, it is on time (The safest bet is to submit it on Thursday sometime). Solutions can be handwritten, but all submissions should be physical copies; no electronic submissions to me or the grader please.

Please do not submit your HW in class. (This change was made to enable you to have more time to work on the problem sets.)

Assignments

1. HW 1: Assigned Wed 8 Sep 21. Due in class Thu 16 Sep 21.

   • E2.4
   • E2.9
   • E2.11
   • E2.14
   • E2.29
   • P2–1
   • P2–6

2. HW 2: Assigned Thu 16 Sep 21. Due in the folder by the morning of Fri 24 Sep 21.

   • E2.35
   • E2.40
   • E2.51
   • P2–8
   • P2–14
   • P2–15
   • E3.1
   • E3.6
   • E3.12

3. HW 3: Assigned Thu 23 Sep 21. Due in the folder by the morning of Fri 1 Oct 21.

   • E3.29
   • E3.32 parts f and h.
   • E3.34
   • E3.38
   • E3.61
   • E3.72
   • P3–10
   • P3–14
   • P3–16

4. HW 4: Assigned Sat 2 Oct 21. Due in the folder by the morning of Wed 13 Oct 21.

   • E4.4
   • E4.13 parts b and d.
   • E4.24
   • P3–5
   • P3–6
   • P3–22
   • P4–4
   • P4–5
   • P4–11

5. HW 5: Assigned Thu 7 Oct 21. Due in the folder by the morning of Mon 18 Oct 21 (Deadline Extended).

   • E4.28
   • E4.29
   • E4.38
   • E4.67
   • P4–14 (short explanations only; full details not necessary)
   • P4–20
   • P4–22
   • P4–23
   • P4–26

6. HW 6: Assigned Fri 15 Oct 21. Due in the folder by the morning of Tues 26 Oct 21 (Deadline Extended).

   • E4.78
   • E4.79
   • P4–18
   • P4–25
   • P4–32

7. HW 7: Assigned Wed 17 Nov 21. Due in the folder by the morning of Tues 30 Nov 21 (Deadline Extended).

   • Hatcher, Ch 0 (p.18), 1.
   • Hatcher, Ch 0, 2.
   • Hatcher, Ch 0, 3.
   • Hatcher, Ch 1.1 (p.38), 1.
   • Hatcher, Ch 1.1, 2.
   • Hatcher, Ch 1.1, 4.
   • Hatcher, Ch 1.1, 12.
   • Hatcher, Ch 1.2 (p.52), 1.
   • Hatcher, Ch 1.2 (p.52), 2.

8. HW 8: Assigned Wed 2 Dec 21. This HW will not be collected and graded.

   • Hatcher, Ch 1.2. 21.
   • Hatcher, Ch 1.2. 22.
   • Hatcher, Ch 1.3 (p.79), 1.
   • Hatcher, Ch 1.3, 2.
   • Hatcher, Ch 1.3, 3.
   • Hatcher, Ch 1.3, 4.
   • Hatcher, Ch 1.3, 10.
   • Hatcher, Ch 1.3, 13.
   • Hatcher, Ch 1.3, 14.
   • Extra: use the Wirtinger presentation (from Hatcher 1.2.22) to compute the fundamental groups of the complements of the figure 8 knot and the Conway knot.