Algebraic Topology I
  
Math 618, Spring 2004
    

Lectures: Tuesday and Thursday 3:00 to 4:30 in the David Rittenhouse Laboratory Building room 4N30.

Professor: John Etnyre
Office: 4E5
Phone: 215-898-8472
e-mail: etnyre "at" math .upenn.edu

This is the "first semester" algebraic topology course here at Penn. But a great deal of algebraic topology is already discussed in the first year topology-geometry sequence. So someone looking for an introduction to algebraic topology should try Math 601 in the spring.

The topics for this course will be:

  • Homotopy Theory
    • Homotopy classes of maps between spaces
    • H and H' spaces
    • Homotopy groups
    • Homotopy groups and CW complexes
    • Whitehead's Theorem
    • Hurewicz' Theorem
  • Fibration
    • Locally trivial fibration, vector bundles, principal bundles
    • Serre Fibrations
  • Obstruction Theory
    • Constructing maps between spaces
    • Cohomology and homotopy theory
  • The product structure on cohomology/Poincare Duality
  • Spectral Sequences

The topics and details associated with the last few items will depend on the time we have left after the other topics are covered and the background of the students in the class. The minimal background for the class is familiarity with the fundamental group, covering spaces and homology. I also expect some knowledge of cohomology, but more advanced aspects of cohomology will be reviewed if necessary.

Grading for the class will be based on homework assignments. The assignments will be posted periodically on this web site along with their due date. In addition to the homework assignments I will frequently give exercises during class. I highly encourage you to think about these as well and talk to me if you have questions, but they will not figure into your grade.

You are welcome to talk with other students or faculty while working on the homework, but what you turn in must be your own work. At some point everyone needs to learn TeX or LaTeX so I encourage you to write up your homework using one of these packages, but this is not a requirement. If you would like help getting started with TeX or LaTeX you are welcome to talk to me about it.

  1. Homework 1. Due September 28.
  2. Homework 2. Due October 14.
  3. Homework 3. Due November 18.
  4. Homework 4. Due December 9.