This is second course in algebraic topology. We will focuse on homotopy theory, computational techniques and applications of algebraic topology to problems in topology. A tentative list of topic are

• The product structure on cohomology/Poincare Duality
• 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
  • Characterisitic classes
  • Cohomology and homotopy theory
• Spectral Sequences

Lectures: Tuesday and Thursday 3:05 in MSE 202.
Professor: John Etnyre
Office: Skiles 106
Phone: 404.385.6760
e-mail: etnyre "at" math .gatech.edu

Grading Policy

I will assing informal homework problems, but they will not be graded. I hope everyone will work them and come discuss any questions you have with me. The grade will be based on class attendence and participation.

Textbook

The textbook for this class is Algebraic Topology by Hatcher. The text is available on-line, but is is a fairly inexpensive book and having a hard copy can be a nice reference. There are many good textbooks for algebraic topology, but I just mention one other book you might find useful: Topology and Geometry by Bredon. For the more advanced topics you can find other notes of Hatcher at his web site. In addtion you might like to cosult Lecture Notes in Algebraic Topology by Davis and Kirk.