spectral sequence

A spectral sequence is a mathematical tool used to analyze complex structures by breaking them into simpler, more manageable stages. Think of it as a multi-layered filter that gradually reveals hidden information about the shape or properties of an object. At each stage, certain details are highlighted while others are simplified, allowing mathematicians to compute or understand complicated relationships step-by-step. Spectral sequences are widely used in algebraic topology and related fields to solve problems involving intricate structures that are difficult to understand directly.