Synopsis:

• This course will be an introduction to the major computational tools of algebraic topology: homology and cohomology. Homology is an algebraic gadget associated to a topological space, and it is often computable. In fact, it is one of the best tools we have for understanding spaces. Its more sophisticated cousin, cohomology, has even more structure and provides even richer information.

Text:

• Algebraic Topology, by Allen Hatcher. We will largely draw from Chapters 2 and 3.

Homework: Homework exercises will be assigned weekly to solidify the material in the lectures. You are strongly encouraged to work in groups on the homework, but you must write up your solutions independently.