Math 215B, Spring 2009
Time:
Tuesday & Thursday, 2:10 pm
Place: Room 61 Evans
Professor: Ian Agol
Office Hours: Monday 11:30-12:30 or by appointment
Office: 921 Evans
Announcement: There will be no class next week (4/21 & 4/23).
These classes will be made up finals week (5/12 & 5/14).
Class will meet 2:10-3:30, 740
Evans, on Tuesday 5/12 and Thursday 5/14
Algebraic Topology
Topics: Homotopy theory and characteristic classes
Texts:
Hatcher,
Algebraic Topology
Milnor
& Stasheff, Characteristic Classes
Recommended Reading:
Rotman,
An Introduction to Algebraic Topology
Hatcher,
Vector Bundles & K-theory
Suggested viewing:
Outside In: everting the sphere
Assignment 1, due Tuesday 1/27: Hatcher p. 358, #2, 3, 4
Assignment 2, due Tuesday 2/3: Hatcher p. 358 #8, 11
1/29: Review the Homotopy Extension Property (pp. 14-15 Hatcher), and
CW complexes (Appendix A, Theorem A.1)
Assignment 3, due Tuesday 2/10: Hatcher p. 359 #19, p. 389 #1
Assignment 4, due Tuesday 2/17: Hatcher p. 389 #4, 7
Assignment 5, due Tuesday 2/24: Hatcher p. 392 #31, 32, 33
Assignment 6, due Tuesday 3/3: Hatcher p. 392 #39, p. 419 #2
Assignment 7, due Tuesday 3/10: Hatcher p. 419 #4, Milnor-Stasheff, p.
11 #1-C
Assignment 8, due Tuesday 3/17: Milnor-Stasheff, problems 2-A, 3-F
Suggested reading: Section 6-4, Munkres
Assignment 9, due Tuesday 3/31: Milnor-Stasheff, problems 4-B, 5-C
Assignment 10, due Tuesday 4/7: Milnor-Stasheff, problems 6-B, 7-B
Review the cross product and Kunneth formula, p. 218 Hatcher
Assignment 11, due Tuesday 4/28: Hatcher
problem 4.D.6
Read Appendix 4.D of Hatcher's Algebraic Topology.
Read Chapter 3 of Hatcher's Vector Bundles & K-Theory
(4/27: you may put off doing 9-A until the next assignment since we
haven't discussed
properties of the Euler class yet).
Assignment 12, due Tuesday 5/5: 9-A, 11-D (only do this problem for
orientable 3-manifolds)
Notes
on the Euler class by Hutchings
Assignment 13, due Thursday 5/14: p. 97, #1 Vector
Bundles & K-Theory