Requirements/prerequisites:

Duration: 19 weeks

Number of lectures per week: 3

Assessment: Weekly homework assignments during 2009 contribute up to 10% of the final mark.

End-of-year Examination: 3-hour end of year exam

Description:

• Quick tour of Algebraic Topology

  Cell Complexes, Homotopy, Homology and cohomology, Spectral Sequences

• Vector Bundles and Associated Fiber Bundles

• Characteristic Classes

• Ring Structure of K(X)

• Bott Periodicity

• Division Algebras and Parallelizable Spheres

• Dirac Operator and its Index

Textbooks:

1. Hajime Sato, Algebraic Topology: An Intuitive Approach, Translations of Mathematical Monographs, Vol. 183 American Mathematical Society 1999 ISBN: 0-8218-1046-4

2. Allen Hatcher, Vector Bundles and K-Theory, (see http://www.math.cornell.edu/~hatcher/VBKT/VBpage.html).

Mar 31, 2009