Instructor: Ko Honda
Office: KAP 406E
E-mail: kohonda at usc dot edu with the first o removed.
Telephone: 213-740-3785
URL: http://rcf.usc.edu/~khonda

Topics

1. Homotopy theory:  fundamental group, covering spaces, Van Kampen's theorem, higher homotopy groups, computations.
2. Homology theory: singular homology, simplicial homology, homotopy invariance, relative homology, excision and Mayer-Vietoris, functoriality, relationship to the fundamental group, applications.
   
3. Cohomology theory: universal coefficient theorem, cup product, Poincare duality.
   

• Hatcher, Algebraic Topology, Cambridge University Press.  Also available for free at http://www.math.cornell.edu/~hatcher/

• Greenberg and Harper, Algebraic Topology.
  

Prerequisites

• Math 440 (undergraduate topology) or equivalent, i.e., some knowledge of algebra and point-set topology.

There will be weekly problem sets.  Currently, I expect to hand out problems sets every Monday, to be turned in the following Monday.  (Of course, there may be exceptional weeks.)  The problem sets count for a large percentage of your total grade (approximately 70%).  You may work with others or consult other textbooks, but the homework you turn in must be written by you, in your own words, and you must cite your sources used and your collaborators!

Final examination

There will be a take-home final.  This will be approximately 30% of your final grade.