Plan

I will lecture on the theory and applications of spectral sequences, with particular emphasis on the Adams spectral sequence calculating the stable homotopy groups of spheres.

• What is a spectral sequence?
• Convergence, exact couples
• Products, Cartan-Eilenberg systems
• Homological algebra, derived functors
• The stable homotopy category, orthogonal spectra
• The Adams spectral sequence
• The sphere spectrum
• Topological K-theory
• Bordism
• Topological modular forms