Mini Course: Spectral Sequences

Spring 2005

This mini course will be a complete introduction to spectral sequences and their applications.

Topics to be covered include:

• the spectral sequence of a filtered complex
• the Leray-Serre spectral sequence
• convergence, edge homomorphisms, transgression
• the Mayer-Vietoris spectral sequence
• integral cohomology of U(n) and BU(n)
• Chen classes
• homology and cohomology of loop spaces
• applications to algebra

• E. Spanier: Algebraic topology, Springer-Verlag, 1981.
• P. Griffiths, J. Morgan: Rational homotopy theory and differential forms, Progress in Mathematics, 16. Birkhäuser, 1981.
• J. McCleary: A user's guide to spectral sequences, Second edition. Cambridge Studies in Advanced Mathematics, 58. Cambridge University Press, 2001.