Snaith's theorem

Snaith's theorem is a result in algebraic topology, particularly in the area of stable homotopy theory. It provides a way to relate different kinds of stable homotopy groups, particularly those associated with certain spectra. Specifically, Snaith's theorem states that for the sphere spectrum \( S \), the stable homotopy groups of \( S \) can be expressed in terms of the homotopy groups of a loop space.