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 .
Relation to the Blakers-Massey theorem
The Frudenthal suspension theorem is a special case of the Blakers-Massey theorem.
A formalization in homotopy type theory in Agda is in
Revised on September 29, 2013 16:23:33
by Urs Schreiber