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