Spectral sequences have a reputation of being difficult (I have absolutely no idea why :P).Even the very name ’Spectral Sequence’ can be quite imposing and terrifying to some mathematicians.Spectral sequences are a major tool from Homological Algebra, originally they were designed to calculate the homology groups of loop spaces. They were introduced by Leray in the 1940’s, they are a great device which encodes a lot of information about homology of rather complicated spaces.
In this talk, I will introduce spectral sequences, and how to construct one. I will do some examples to explain the application of spectral sequences to algebraic and topological problems, and hopefully I will convince you that they are useful and tell why you shouldn’t be frightened when they come up in a seminar.