## Homework for Math 622

• For Wednesday, January 16.
On Wednesday, Jan 23, turn in p. 7 #1 (You may omit part (3).) , 2
• For Friday, January 18.
• For Wednesday, January 23.
There is no class Monday January 21, for MLK Day.
On Wednesday, Jan 23, turn in p. 7 #1 (You may omit part (3).) , 2
• For Friday, January 25.
On Wednesday, January 30, turn in p. 14 # 1, 5; p. 19 # 1bc.
• For Friday, February 1.
On Wednesday, February 6, turn in p. 19 # 2(for 3.11 and 3.13), 3; p. 26 # 3ab.
• For Monday, February 4.
• For Friday, February 8.
On Wednesday, February 13 turn in: p. 26 # 3cd; p. 33 # 4, 5, 6.
• For Friday, February 15.
On Wednesday, February 20 turn in: p. 40 # 3, 6a.
• For Monday, February 18.
• For Friday, February 22.
On Wednesday, February 27 turn in HW # 6: p. 43 # 1; p. 46 # 1; p. 51 # 2.
• For Monday, February 25.
• For Wednesday, February 27.
• For Friday, March 1.
On Wednesday, March 6 turn in: HW # 7: p. 52 # 3, p. 70 # 2 [just do it for g and h], 3.
• For Monday, March 4.
• For Wednesday, March 6.
Turn in: HW # 7: p. 52 # 3, p. 70 # 2 [just do it for g and h], 3.
• For Friday, March 8.
On Wednesday, March 13 turn in: p. 135-136 # 2ab, 3, 6. [For #2b see p. 23. In # 6 use the Klein bottle on page 37, where C = z1 and A = w1.]
• For Monday, March11.
• For Wednesday, March 13.
• For Friday, March 15.
On Wednesday March 27 turn in p. 141 # 1, 3, 6a (You may assume r is simplicial. A retraction r: X to A, where A is a subspace of X, is a continuous map r: X to A such that r i = 1_A where i is the inclusion map i: A to X and 1_A is the identity map on A. )
• For Monday, March 25.
• For Wednesday, March 27.
Read pp. 162-167. Turn in p. 141 # 1, 3, 6a.
• For Friday, March 29.
For Wednesday, April 3 turn in p. 144 # 1bc, 2; p. 168 # 1.
• For Friday, April 5.
On Wednesday, April 10 turn in p. 175 # 3. Also turn in: Find the singular homology groups for all p of (a) Moebius strip (b) a tree (c) S1 cross S1. [Hint: first find the homology groups of (S1 cross I, S1 cross {0,1}).]
• For Monday, April 8.
• For Wednesday, April 10.
There is also an assignment due.
• For Friday, April 12.
The final exam schedule is Tuesday, May 7, 12:00 - 2:00. I plan to have an individual oral final exam.
On Wednesday, April 17, turn in:
(1) Let S1 be the unit circle in the complex plane. Define T: Delta1 to S1 by T(t) = cos(2št) + i sin(2št). We know that the singular homology class of T generates H1(S1).
Define f: S1 to S1 by f(z)= z^2.
(a) Prove that f#(T) is homologous to 2 T by giving an explicit singular 2 simplex with boundary 2T - f#(T).
(b) Find deg(f).
(2) p.121 # 2.
(3) p. 250 # 1.
• For Monday, April 15.