MAT 762 - Algebraic Topology - Fall 2013

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
  • PoincarĂ© 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 Assignments:

Further Reading:

  • 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.