Freudenthal suspension theorem
Paths and cylinders
The Freudenthal suspension theorem (Hans Freudenthal, 1937) is the following theorem about homotopy groups of spheres:
The suspension homomorphism is an isomorphism for .
In this statement, one can replace with any -connected space while replacing with the corresponding suspension .
This theorem justifies introducing the stable homotopy groups of spheres , as well as stable homotopy groups , both independent of where .
A formalization in homotopy type theory in Agda is in
Revised on February 25, 2013 12:15:09
by Urs Schreiber