*Ma 151c* - Algebraic topology 3; Spring 2011

### Instructor: Danny Calegari

### Grader: Steven Frankel (email sfrankel)

### MWF 2:00-3:00 257 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 course continues on from 151ab. We will study characteristic classes and
vector bundles, with a view to topological applications; also we will study spectral sequences.

### Notices:

The classes on Wednesday and Friday April 27 and 29 will be taught by Steven Frankel.

### Homework (all homework is from Milnor's book except where indicated):

- week 1, due Friday April 8: these problems plus Milnor 1-A, 1-B, 1-C, 2-C, 2-E, 3-A
- week 2, due Friday April 15: Milnor 3-D, 3-E, 4-B, 4-D, 5-B, 5-C
- week 3, due Friday April 22: Milnor 6-C, 7-A, 7-B, 7-C, 8-A, 8-B
- week 4, due Friday April 29: Milnor 9-B, 9-C, 11-C, 11-D, 12-B, 12-D
- week 5 MIDTERM, due Friday May 6: Milnor 3-F, 4-C, 6-B, 11-E, 13-E; Hatcher VBKT Chapter 3 Exercise 3 (page 97)
- week 6, due Friday May 13: Milnor 13-F, 14-B, 14-E, 15-B, 16-C, 16-D
- week 7, due Friday May 20: Milnor 19-A; Hatcher SSAT 1.1 Exercises 1, 2 (page 23) 1.2 Exercise 2 (page 51)
- week 8 FINAL, due Friday May 27: Milnor 13-D, 14-C, 15-C, 16-E, 19-B; Hatcher SSAT 1.2 Exercise 3 (page 51)

### References:

- Milnor,
*Characteristic Classes*, Princeton University Press Annals of Math. Studies 76, 1974
- Hatcher,
*Algebraic Topology*, Cambridge University Press, 2002 (also available from author's webpage)
- Hatcher,
*Vector Bundles and K theory (VBKT)*, available from author's webpage
- Hatcher,
*Spectral Sequences in Algebraic Topology (SSAT)*, available from author's webpage
- Husemoller,
*Fibre Bundles*, Springer-Verlag GTM volume 20 (second edition 1975)
- Griffiths and Morgan,
*Rational Homotopy Theory and Differential Forms*, Birkhauser Progress in Mathematics 16, Birkhauser, 1981
- books on reserve
- Notes on rational homotopy theory (summary of some of Chapters 8-11 of Griffiths-Morgan)