Spectral sequences

Spectral sequences are a mathematical tool used to analyze complex structures by breaking them down into more manageable stages. Think of them as a multi-layered process that gradually reveals the intricate features of a mathematical object, much like peeling an onion layer by layer. At each stage, partial information is refined and improved, leading to a clearer understanding of the whole. They are often employed in algebraic topology and related fields to compute difficult invariants by systematically approximating and converging toward the final result through a sequence of simpler calculations.