The Serre Spectral Sequence
Some of my earliest independent academic writing, written as my final project for Math 215A: algebraic topology. I had recently finished reading the first half of Wiebel’s An Introduction to Homological Algebra when I wrote this, so spectral sequences had been top-of-brain for me at the time. The paper introduces spectral sequences from “first principles,” assuming some topological and algebraic maturity, and describes the construction of the Serre spectral sequence as applied to Serre fibrations. I then derive a few topological consequences: the relationship between the connectedness of the base and fiber spaces of a fibration, the Wang and Gysin sequences, and the classification of the homology of loop spaces.