 Stable homotopy theory

Stable homotopy theory studies topological spectra, which retain the information that persists under repeated reduced suspension. Its stable homotopy category admits invertible suspension of spectra and exact cofiber sequences of spectra.

Stable homotopy theory is a field in algebraic topology that studies the properties of spaces and spectra that remain invariant under suspensions (or shifts). It arises from the observation that the homotopy groups of spheres, which are foundational objects in topology, exhibit a highly structured and rich behavior when examined in a stable context.