Stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor.

Stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor.

A founding result was the Freudenthal suspension theorem, which states that for a given CW-complex $X$ the $(n+i)$-th homotopy group of its $i$-th iterated suspension, $π_{n+i} (Σ^iX)$, becomes stable (i.e., isomorphic after further iteration) for large but finite values of $i$.