Padelford C-554

Dept. of Mathematics, Box 354350

University of Washington

Seattle WA 98195

devinatz@math.washington.edu

(206)685-4777 - office phone number

General Information

Homework 1: Read Chapter 2 in the text and do Problems 2-1 bce, 2-3, 2-10, 2-12, 2-13, and 2-15. This assignment is due Wednesday, October 5.

Homework 2: Read Chapter 3 in the text and do Problems 3-1, 3-6, 3-14, 3-16, 3-22, and 3-23 (prove what you need from 3-5). This assignment is due Friday, October 14.

Homework 3: Read Chapter 4 in the text and do Problems 4-1, 4-13, 4-23, 4-24, 4-26, and 4-27. This assignment is due Monday, October 24.

Homework 4: For this assignment, I suggest you use your lecture notes as the primary reference and fill in the gaps by reading from Chapters 5 and 6 as needed. Do problems 5-3 (assume part a but convince yourself that you know how to prove it), 5-7, and 5-9 (you may replace "CW-complex" by "Euclidean simplicial complex" although the proof is no more difficult in the more general case. As a hint, proceed by induction on the skeleta using the fact that the polyhedron of the (i+1)-skeleton is obtained from the polyhedron of the i-skeleton by adding (i+1)-cells.) This assignment is due Monday, October 31.

Homework 5: Read Chapter 7 in the text and do Problems 7-1, 7-2, 7-5, 7-13, 7-14, and 7-15. In 7-15, it's ok to use pictures to indicate some of the spaces and homotopies involved as long as they are clear. Note also that Problem 5-4 as stated is not true. You may use a special case of 5-4 without proof as long as it's obvious. This assignment is due Monday, November 14.

Homework 6: Read Chapter 8 --- and Chapter 11 up to page 283 --- and do Problems 8-1, 8-2, 8-5, 8-6, and 8-7. You may use the result of Problem 8-4 without proof, but you should know how to prove it if you use it. This assignment is due Monday, November 21. N.B. We will not be discussing Chapter 9 in class but will be using it when we discuss Chapter 10 after this assignment. You should read it as needed.

Homework 7: Read Chapter 10 --- you may skip the section on graphs --- and chapter 9 as needed. Do Problems 10-2, 10-6, 10-9, and 10-15. This assignment is due Wednesday, November 30.

Homework 8: Read Chapter 11 and Chapter 12 up to page 311. Then do Problems 11-4 (clear pictures are ok), 11-11, 11-12, 11-14, and 11-21 (prove what you need from 11-20). This assignment is due Friday, December 9.

General Information

Homework 1: Read Chapter 12 up to p.322 and do Problems 12-1, 12-2, 12-6, 12-14, and 12-15. You need not prove that q is a covering map in 12-2. This assignment is due Wednesday, January 11.

Homework 2: This assignment is due Monday, January 23.

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