In mathematics, stable homotopy theory is the 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 given any pointed space X {\displaystyle X} , the homotopy groups π n + k ( Σ n X ) {\displaystyle \pi _{n+k}(\Sigma ^{n}X)} stabilize for n {\displaystyle n} sufficiently large.
In mathematics, stable homotopy theory is the 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 given any pointed space X {\displaystyle X} , the homotopy groups π n + k ( Σ n X ) {\displaystyle \pi _{n+k}(\Sigma ^{n}X)} stabilize for n {\displaystyle n} sufficiently large.
Source: Wikipedia "Stable homotopy theory" · CC BY-SA 4.0
Share this article: X · Bluesky