*Ma 151a* - Algebraic topology 1; Fall 2007

### Instructor: Danny Calegari

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

### MWF 2-3 11 Downs

### Grading policy:

Homework is given out in class on Friday. This homework is due at noon (outside the office) the following Friday. 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 12 October: section 1.1, problems 2, 3, 6; section 1.3, problem 1
- week 2, due Friday 19 October: section 1.1, problems 7, 10; section 1.2,
problems 9, 22; section 1.3, problems 6, 7
- week 3, due Friday 26 October: section 0, problems 16, 17; section 1.3,
problems 9, 10, 12, 15
- week 4, due Friday 2 November: section 1.3, problems 14, 21, 30, 32;
section 1.B, problems 1, 6
- week 5, MIDTERM due Friday 9 November: section 1.1, problem 17; section 1.2, problem 21; section 1.3, problem 18; section 1.A, problem 8; section 1.B,
problem 8
- week 6, due Friday 16 November: section 2.1, problems 1, 5, 8, 10, 11, 12
- week 7, due Monday 26 November: section 2.1, problems 15, 21, 29; section 2.2, problems 2, 8, 12
- week 8, FINAL due Wednesday 5 December: section 2.1, problem 28; section
2.2, problems 17, 25, 33; section 2.B, problem 9

### References:

- Hatcher,
*Algebraic Topology*, Cambridge University Press, 2002 (also available from author's webpage)
- MacLane,
*Homology*, Springer-Verlag, Classics in Mathematics, 1995