Spectral sequences

Spectral sequences are a powerful mathematical tool used primarily in algebraic topology, homological algebra, and algebraic geometry. They provide a systematic method for computing homology groups, cohomology groups, or other related invariants of topological spaces or algebraic objects. ### Definition and Construction A spectral sequence consists of a sequence of pages (or terms), each represented as a collection of abelian groups or modules, along with differentials that relate these groups across the pages.