Homotopy excision theorem
In algebraic topology, the homotopy excision theorem offers a substitute for the absence of excision in homotopy theory. More precisely, let be an excisive triad with nonempty, and suppose the pair is -connected,, and the pair is -connected,. Then the map induced by the inclusion,
is bijective for and is surjective for.
A geometric proof is given in a book by Tammo tom Dieck.
This result should also be seen as a consequence of the Blakers–Massey theorem, the most general form of which, dealing with the non-simply-connected case.
The most important consequence is the Freudenthal suspension theorem.
