The course will cover parts of Chapter 4 and 5 of the textbook, as well as additional topics depending on time and interest.
After a brief review of MAT 761, we will discuss the following material:
- Cohomology of a Chain Complex and Universal Coefficient Theorem
- Singular Cohomology and Cup Product
- Orientations and Homology
- Poincaré Duality and Intersection Product
- Applications of Cohomology
- Higher Homotopy Groups
- Additional Topics (e.g. Obstruction Theory, Fiber Bundles, Spectral Sequences, Characteristic Classes, De Rham Cohomology, Sheaf Theory, Knot Theory)
More information can be found below:
- Text: Allen Hatcher, Algebraic Topology, Cambridge University Press, 2001. Online Version
- Classes: Tu and Th, 12:30 - 1:50, 306 Carnegie
- Office Hours: Tu 5 PM - 6 PM and Th 10 AM - 11:30 AM
- Academic Integrity: See Syracuse University's Academic Integrity Policy
- Students with Disabilities: If you believe you need an accommodation for a disability, please talk to me at the beginning of the semester or contact the Office of Disability Services (ODS), located in Suite 303 of 804 University Avenue, or call (315) 443-4498
- Religious Observances Notification: Students who will be observing religious holidays during the semester are required to fill out their notification form on MySlice by the end of the second week of classes.
A PDF version of the syllabus can be found here.
- Homework 1, due in class on Tuesday, September 17
- Homework 2, due in class on Tuesday, October 1
- Homework 3, due in class on Thursday, October 17
- Homework 4, due in class on Tuesday, November 12
- Homework 5, due in class on Tuesday, December 3
- William S. Massey, A Basic Course in Algebraic Topology, Springer, 1991.
(Chapter VII contains an introduction to cubical singular homology)
- Charles A. Weibel, An introduction to homological algebra, Cambridge
University Press, 1995. (Introduction to modules, complexes, functors, etc.)
- John M. Lee, Introduction to Smooth Manifolds, Springer, 2002.