*Ma 151a* - Algebraic topology 1; Fall 2009

### Instructor: Danny Calegari

### Grader: Yi-Chih Chiu (email ycchiu)

### MWF 2-3 257 Sloan

### Grading policy:

Homework is posted on the web at regular intervals. This homework is due at 2 pm (outside the office) on the day indicated. There will be a midterm
(in place of one of the homework assignments) and a final. The exams together will be worth 50% of the grade, and the homework 50%. The only difference
between an exam and a regular homework is that collaboration is not allowed.

### Description of course:

This is the first course in the year-long graduate
sequence in topology. The main topics covered are fundamental
group, covering spaces, and homology. This comprises roughly
Chapters 0-2 of the required text, which is
Algebraic
Topology by Allen Hatcher. The book is available online, which is
very convenient, but it is priced so reasonably that it would be foolish
not to buy a copy.
There are not many prerequisites beyond some point-set topology,
undergraduate analysis, and a certain amount of mathematical
maturity. The Caltech class Ma 108a would suffice as background.

### Homework (all homework is from Hatcher's book):

- week 1, due Friday 9 October: section 0, problems 2, 3, 6, 9
- week 2, due Friday 16 October: section 1.1, problems 3, 6, 8, 12, 16, 17
- week 3, due Friday 23 October: section 1.1, problem 20; section 1.2, problems 1, 3, 9, 14, 22
- week 4, due Friday 30 October: section 1.3, problems 3, 6, 13, 15, 26, 32
- week 5, MIDTERM, due Friday 6 November: section 0, problem 21; section 1.1, problem 10; section 1.2, problems 16, 17; section 1.3, problem 12; section 1.B, problem 1
- week 6, due Friday 13 November: section 2.1, problems 3, 6, 8, 10, 11, 14
- week 7, due Friday 20 November: section 2.1, problems 22, 28; section 2.2, problems 8, 11, 16, 25
- week 8, due Wednesday 25 November: section 2.2, problems 30, 40, 42
- week 9, FINAL, due Friday 4 December: section 2.1, problems 26, 27; section 2.2, problems 1, 35, 38; section 2.B, problem 1

### References:

- Hatcher,
*Algebraic Topology*, Cambridge University Press, 2002 (also available from author's webpage)
- MacLane,
*Homology*, Springer-Verlag, Classics in Mathematics, 1995
- Rolfsen,
*Knots and Links*, Publish or Perish, 1990