Stable homotopy theory

Summary

Stable homotopy theory is the part of homotopy theory that studies the phenomena that do not change under iterated suspension. By the Freudenthal suspension theorem, the homotopy groups of $\Sigma^k X$ stabilize as $k$ grows. The stable values are often more regular than the unstable ones. Its natural objects are spectra, which represent generalized cohomology theories, and its main computational problem is the stable homotopy groups of spheres.