Ma 151a - Algebraic topology 1; Fall 2008

Instructor: Danny Calegari

Grader: Yi Chih Chiu (email ycchiu)

MWF 2-3 257 Sloan

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 10th October: section 1.1, problems 2, 3, 6; section 1.3, problem 1
• week 2, due Friday 17th October: section 1.1, problems 5, 10; section 1.2, problems 9, 10, 21, 22
• week 3, due Friday 24th October: section 0, problems 16, 22; section 1.2, problems 14, 18; section 1.3, problems 9, 10;
• week 4, due Friday 31st October: section 1.3, problems 12, 13, 30, 32; section 1.B, problem 1; plus these problems
• week 5, MIDTERM due Friday 7 November: section 1.1, problems 12, 13; section 1.2, problems 15, 20; section 1.3, problems 6, 21
• week 6, due Friday 14 November: section 2.1, problems 1, 5, 8, 10, 11, 12
• week 7, due Friday 21 November: section 2.1, problems 15, 21, 29; section 2.2, problems 2, 8, 17
• week 8, FINAL due Wednesday 3 December: section 2.2, problems 12, 25, 33, 35, 37, 42

References:

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