Stable homotopy theory

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In mathematics, stable homotopy theory is a branch of algebraic topology. Stability here refers to the application of the suspension functor. A founding result was the Freudenthal suspension theorem. In general, stable homotopy theory tries to isolate the phenomena of homotopy theory that are essentially unchanged after sufficiently many applications of suspension, or then become more perspicuous.

In the modern treatment of stable homotopy, spaces are typically replaced by spectra.

One of the most important problems in stable homotopy theory is the computation of stable homotopy groups of spheres.

[edit] References

• Stable homotopy Theory , by J.F.Adams, Springer-Verlag Lecture Notes in Mathematics No.3 (1969)
• J.P.May ,Stable Algebraic Topology, 1945-1966