Math 533, Algebraic Topology II.
Topics
This is a sequel to Math 532. It will deviate somewhat
from the catalog description, but will still
cover more advanced topics in
homology and cohomology of topological spaces.
We will start with a review of CW complexes and cellular
(co)homology, and discuss mapping cones.
Then we will focus on K-theory for topological spaces,
which is a nonstandard cohomology getting lots of attention
in many areas of physics. This involves classifying
vector bundles over spaces. Tools from geometry
often assist with this classification.
Additional topics will be selected after gauging
student interest, from topics such as:
- Shape theory.
- Alexander–Spanier cohomology.
- The universal coefficient theorem.
Textbook
We will have at two texts.
The bookstore will probably provide both a hardcover and an
e-book option for the book by Park.
Be sure your UNM email account is working and you have a way to check it daily. There
are limitations on how I can send to non-UNM email accounts.
We will be utilizing
UNM-Learn . Before classes start is a good
time to discover if there are techical or accessibility issues related to your
viewing material at UNM-Learn.
It is too slow and difficult to upload videos to UNM-Learn, so here are
some of the videos shown in class.
From Lecture 1, Moore_2.avi, Moore_4.avi,
curveInMoore4.avi, Moore4path2.avi,
Moore4path.avi.
From Lecture 3, mappingCone1.avi,
mappingCone2.avi.