
The aim of Math 148 is to provide an introduction to algebraic topology through lowdimensional geometric objects like surfaces and graphs. Basic algebraic invariants like the Euler characteristic and the fundamental group are used to study and classify these spaces and their covering spaces.
"Algebraic Topology: An Introduction" by W.S. Massey, SpringerVerlag Graduate Texts in Mathematics, 1967. (Available at the bookstore).
Triangulations and classification of surfaces. Euler characteristic.
Fundamental group, Brouwer Fixed Point Theorem, homotopy equivalence.
Free groups, amalgamation, Van Kampen's Theorem. Covering spaces:
definitions and classification. Graphs and trees.
This material is covered in the first six chapters of the text.
For a detailed syllabus, click here:
Syllabus
January 9th: Since the text assumes familiarity with the notions of a topological space, open sets, and continuity, we are providing some notes that cover the main definitions, as described in the first couple of lectures, here.
February 8: The midterm will be held on the evening of Thursday, February 16, from 7:309:30 pm in Room 380380F. It will cover the material in the text from Chapters 1 and 2 (excluding section 13 in Chapter 1), and the material about groups, as discussed in class (essentially sections 46 in Chapter 3 of the text). You should also know the statements and be able to apply the versions of Van Kampen's Theorem presented in class.
February 9: Here is a more detailed list of the topics for which you will be responsible on the midterm. Note that no books, notes, or electronic devices will be allowed during this exam.
February 23: Here are a few pages from Dale Rolfsen's book "Knots and Links" for reference concerning the lectures and homework on knots. It's a wonderful book that you should take a look at sometime.
February 25: Problem 10 on homework number 7 was edited slightly.
March 17: Here is a list of the topics for which you will be responsible on the final exam. You should also refer to the review sheet for the midterm and here is a copy of the midterm for reference. Note that no books, notes, or electronic devices will be allowed during the final exam.
March 18: The final exam will be held on the morning of Thursday, March 23, from 8:3011:30 am in Room 380380D. See the review sheet above for the topics to be covered.
Homework will be due in class each Wednesday, the first assignment being due on Wednesday, January 18th. Late work will not be accepted. The homework assignments will be posted approximately 1 week before they are due.
Click here for Homework assignments.
Homework Solutions should appear here a few days after the assignment is due.
They will be accessible from the Homework Assignments page.
There will be a Midterm and a Final.
Midterm: Thursday, February 16,
7:309:30 p.m., room 380380F
Final: Thursday, March 23, 8:3011:30 a.m.,
room 380380D
The time and date of the Final Exam is fixed by the Registrar and cannot
be changed.
25% Homework
30% Midterm
45% Final