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