# Ma 151b - Algebraic topology 2; Winter 2007

### MWF 10:00-11:00 153 Sloan

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. I will be traveling during the week Feb 19-23 and Feb 28-Mar 2; Rupert Venzke will teach the class Feb 19-23. The classes Feb 28-Mar 2 might be rescheduled, if possible.

### Description of course:

This course continues on from 151a. We will study cohomology and higher homotopy groups.

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

• week 1, due Friday 12 January: section 3.1, problems 1, 6(a), 10, 11; section 3.2, problems 1,3
• week 2, due Friday 19 January: section 3.2, problems 7,8,11,13,14
• week 3, due Friday 26 January: section 3.2, problems 15,16; section 3.3, problems 1,8,9,10,11
• week 4, due Friday 2 February: section 3.3, problems 6,24,25,26,29 (for 29, use the results of 27 and 28 without proof)
• week 5, due Friday 9 February: section 3.3, problems 14,16,17; section 4.1, problems 3,4,5
• week 6, MIDTERM, due Friday 16 February: section 3.1, problem 13; section 3.2, problem 4 (Lefschetz fixed point theorem is 2C.3); section 3.3, problem 33; section 4.1, problem 11
• week 7, due Friday 23 February: section 4.1, problems 12, 15; section 4.2, problems 1, 7
• week 8, due Friday 2 March: section 4.2, problems 12, 28, 31, 34, 38
• week 9, FINAL, due Friday 16 March: section 4.1, problems 18, 22 (for 22, prove the existence of a weak homotopy equivalence to a CW complex with countably many cells); section 4.2, problems 5, 19; section 4.3, problems 1, 11

### References:

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