Math 524: Algebraic Topology
Course Description
Algebraic
topology uses techniques from abstract algebra to study
how (topological) spaces are connected. Most often,
the algebraic structures used are groups
(but more elaborate structures such as rings or modules also
arise). A typical approach projects continuous maps between
topological spaces onto homomorphisms between the
corresponding groups. This course will introduce basic
concepts of algebraic topology at the first-year graduate
level.
We will follow mostly the book Elements of
Algebraic Topology by James R.~Munkres, and cover in a
fair bit of detail the topics on homology of simplicial
complexes, relative homology, cohomology, and the basics of
duality in manifolds (selected Sections from Chapters
1–5 and 8). Another popular book
is Algebraic
Topology by Allen Hatcher which could be used as a
reference. We will not have the time to cover topics
related to the fundamental group. We will stress geometric
motivations as well as applications (where relevant)
throughout the course.
Prerequisites: Some background in general topology as
well as abstract algebra, both at the undergraduate level,
will be assumed. In particular, familiarity with the
concepts of continuous functions, connectedness, and
compactness, as well as with the concepts of groups,
homomorphisms, fields, and vector spaces will be helpful to
follow the course. But no particularly deep theorems from
these topics will be needed. Some flexibility could be
afforded as far as this background is concerned—please
contact the instructor if you have doubts.
Announcements
Fri, Aug 18: | The class will meet TTh 1:30-2:45 pm in Spark 333 (Pullman) and VECS 309 (Vancouver). |
Mon, Aug 28: | Tomorrow's (Tue, Aug 29) lecture will originate in Pullman. |
Sun, Sep 17: | No regular lecture on Tuesday (Sep 19). A make-up video lecture has been posted. |
Mon, Nov 27: | This week's (Nov 28, 30) lectures will originate in Pullman. |