440-3 - Geometry/Topology: Cohomology

Monday, Wednesday, Friday 10:00pm - 10:50pm, Lunt 103
Webpage: http://www.math.northwestern.edu/~gangliu/4403.html

Instructor:

Gang Liu
Email: gangliu@math.northwestern.edu
Office: Lunt 229

Office hours:

Mondays, 1:00pm - 2:00pm
or by appointment

Course Description:

This course is an introduction to cohomology. See the syllabus below for more detailed content information.

Textbook:

A. Hatcher - Algebraic Topology, Cambridge University Press 2001. [PDF]

In the first part of the course, we will also use
R. Bott, L.W. Tu - Differential forms in algebraic topology (Third edition), Springer 1995.
J.M.Lee - Introduction to Smooth Manifolds (Second edition), Springer 2012.

Homework:

There will be weekly written assignments which can be found below along with the due date and time. Problem sets are due on Wednesdays in class, except as marked below. The solutions will be posted below.

Grading and Final:

The class grades will be based on the weekly homework, on a midterm and on the final exam. Both will be take-home exams.


Daily Schedule:

This is a tentative syllabus and it is likely to change as the course progresses.

Due April 11 in class
Date Topics Covered Remarks
April. 3, 4, 6 de Rham Cohomology Homework 1
Solution
April. 9, 11, 13 Mayer-Vietoris Sequence, Poincare duality Homework 2
Due April 18 in class
Solution
April. 16, 18, 20 Kunneth formula, Lefschetz fix pt thm Homework 3
Due April 25 in class(ignore the date in pdf!)
April. 23, 25, 27 Thom isomorphism, Euler class