Homework Assignments for
M382C, Algebraic Topology
(last revised November 1)

The due dates were originally written assuming we were collecting homework on  Fridays.  Starting November 5, however, homework is due on Mondays.

Homework # 1: (due September 7)
Show that each of the following sets (given a reasonable topology) is a manifold.  What is the dimension of each one?  Which are orientable?

1)    The set of all lines through the origin in R^4.  (This manifold is called RP^3).
2)    The set of all lines through the origin in R^5 (called RP^4)
3)    The set of all planes through the origin in R^4.
4)    The set of all lines (not necessarily through the origin) in R^3.
4)    The set of all complex triples (z1, z2, z3) such that z1^2 + z2^2 +z3^2 = 1.
5)    The set of all invertible 2x2 real matrices.

Exercises 5.1, 7.1, 7.2 and 7.6 (cases 7.1 and 7.2 only) from Chapter 1.

Homework # 2: (due September 14)

Chapter 1: 8.1, 8.3, 8.8, 8.9 (use Euler!)
Chapter 2: 3.1, 3.3,  4.5,  4.6, 4.8, 4.9, 5.1

Homework # 3: (due September 21)
Chapter 2: 7.1, 7.2,  7.4, 7.5, 8.1
Chapter 3: 3.1, 3.3, 3.4

Homework # 4: (due September 28)
Chapter 3: 4.1, 4.3, 4.7, 4.8, 5.3, 6.1,

Homework # 5: (due October 5)
Chapter 4: 3.1, 3.2, 3.3, 4.1, 5.1, 5.2, 5.3

Suggested homework to help study for midterm: (do not turn in)
Chapter 4: 5.4, 5.5, 5.6, 6.1

Homework # 6: (due October 19)
Chapter 5: 2.4, 5.1, 6.1, 6.2, 6.4, 6.5

Homework # 7: (due October 26)
Chapter 5: 7.1, 7.2, 8.1, 8.2, 8.3, 9.3, 10.1

Homework #8: (due November 5)
Chapter 7: 2.1, 3.3, 5.1, 5.2, 5.4, 5.5 (p 172, not 173)

Homework #9: (due November 12)
Chapter 7: 6.2
Chapter 8: 2.1, 2.2, 2.3, 2.5, 2.8, 2.9

Homework #10: (due November 19)
Chapter 8: 3.1, 3.2, 3.7, 4.1, 4.2, 5.1

Homework #11: (due December 3)
TBA