MTH 961


This is the course website for MTH 961. Here is our syllabus.

As of today (3/11/20) this course will meet online for the duration of the semester.

We will have a course meeting on Zoom beginning at 1:30 pm today (Wednesday 3/11). Click here to join the scheduled meeting.



Course text

Characteristic Classes John Milnor and James Stasheff

D2L login page

Other references

Vector Bundles & K-theory Allen Hatcher
Lecture Notes in Algebraic Topology James Davis and Paul Kirk
Characteristic Classes Robert Bruner, Michael Catanzaro and Peter May


Suggested Exercises (from Milnor-Stasheff)

1-A, 1-B, 2-A, 2-D, 3-B, 3-D, 4-D, 4-E

5-E, 6-A, 6-B, 6-C, 6-D, 7-A, 9-A, 9-C

Finish the proof of the following fact:
If M is a smooth compact manifold with oriented tangent bundle and non-trivial Euler class, then TM does not admit any odd dimensional sub-bundles.
(We did the case of orientable sub-bundles in class. Hint: Consider the orientation double cover of M.)
In addition, can you calculate w_1(M)?