**Classes:**TuTh 9:30 - 10:50 AM, 109 Carnegie**Office Hours:**TuTh 3:10 - 4:10 PM and by appointment. I have an open door policy for short to medium questions.**Text:***Algebraic Topology*by Allen Hatcher, Cambridge University Press, 2001**Homework:**Regular homework will be assigned and collected in class. You may discuss the homework problems with your classmates, but the work you turn in should be your own, in your own words.**Course Description:**The course is a continuation of MAT 761 and will cover Chapter 3 of the textbook and parts of Chapter 4. Specifically, the course will cover the following topics:

• Definition of cohomology (singular, simplicial, and cellular)

• Universal Coefficient Theorem

• Properties of cohomology

• Cup product

• Cohomology of product spaces

• Cap product

• Orientations on manifolds

• Poincaré duality, intersection product, Alexander duality

• Smooth manifolds

• Higher homotopy groups

• Additional topics depending on time and interest**Prerequisites:**(MAT 632 and MAT 761) or graduate standing in mathematical sciences.**Course Syllabus:**A PDF version of the course syllabus can be found here.

**Homework Assignments:**

- Homework 1, due in class on Tuesday, September 10
- Homework 2, due in class on Thursday, September 19
- Homework 3, due in class on Tuesday, October 1
- Homework 4, due in class on Thursday, October 10
- Homework 5, due in class on Tuesday, October 22
- Homework 6, due in class on Thursday, October 31
- Homework 7, due in class on Tuesday, November 12
- Homework 8, due in class on Thursday, November 21

**Further Reading:**

- Glen Bredon,
*Topology and Geometry*, Springer GTM, 1993. - Charles Weibel,
*An Introduction to Homological Algebra,*Cambridge University Press, 1995.