440-3 - Geometry/Topology: Cohomology

Monday, Wednesday, Friday 10:00pm - 10:50pm, Lunt 102
Webpage: http://www.math.northwestern.edu/~gangliu/4403.html

Instructor:

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

Office hours:

Wednesdays, 11:00am - 12:00pm
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 Mondays 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 take-home exam.


Daily Schedule:

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

Date Topics Covered Remarks
Mar. 27, 29, 31 de Rham Cohomology Homework 1
Due April 3 in class
Solution
April. 3, 5, 7 Mayer-Vietoris Sequence, Computations Homework 2
Due April 10 in class
Solution
April. 10, 12, 14 Poincare duality, Kunneth formula Homework 3
Due April 17 in class
Solution
April. 17, 19, 21 Lefschetz fixed point theorem, Thom isomorphism Homework 4
Due April 26 in class
Solution
April. 26, 28 Euler class Homework 5
Due May 1 in class
Solution
May 1-5 Midterm midterm
Due May 5 in class
Solution
May 1, 3, 5 Singular homology and cohomology Homework 6
Due May 8 in class
Solution
May 8, 10, 12 Universal Coefficient theorem, Simplicial (co)homology Homework 7
Due May 15 in class
Solution
May 15, 17, 19 Cell homology, degree of maps Homework 8
Due May 24 in class
Solution
May 22, 24, 26 Cup product, Sheaves Homework 9
Due May 31 in class
May 31, June 2 Cech cohomology, De Rham theorem
June 2-10 Final exam Final exam
Due June 10(email preferred)
Solution