Math 215A, Algebraic Topology

UC Berkeley, Fall 2017

Announcements:

Instructor:

Michael Hutchings
hutching@math.berkeley.edu
Office phone: 510-642-4329.
Office: 923 Evans.
Tentative office hours: Thursday 1:00-3:30.

Piazza:

In addition to my office hours, I have set up a piazza page for the course here. Please feel free to ask questions about the course content there.

Textbook:

The textbook for this course is Algebraic Topology by Allen Hatcher. The book with the latest corrections can be legally downloaded for free here.

Homework:

The course grade will be based on homework, which will usually be due a little less than once per week. Collaboration on homework is encouraged but must be acknowledged, and you must write your own solutions. Please write clearly, because your assignments will be peer-graded!

Instructions for peer-grading homework: Write your name, the name of the student whose homework you are grading, and your feedback, all on a separate sheet. Each problem should get 3 points if it is more or less all correct, 2 points if it has some minor problems, 1 point if it has more serious problems, and 0 points if there is no significant progress toward a solution. You are welcome to ask about how to solve the prolems on piazza. Be sure to give constructive comments. An important goal of this exercise is to help everyone improve their mathematical communication skills. Graded homework should be returned one week after it is handed in.

Syllabus:

The goal of this course is to explain how algebraic topology works and how it can be applied to geometric problems. Specifically, we will study the basics of the fundamental group, homology, and cohomology, roughly corresponding to the first three chapters of Hatcher. I will skip some of the more specialized topics in Hatcher (especially in some of the appendices), and will introduce some more geometric topics which are not covered by Hatcher.

What we actually did in class:

Below I will list what we did in each lecture, and where you can read more about it.