Homotopy excision theorem

In algebraic topology, the homotopy excision theorem offers a substitute for the absence of excision in homotopy theory.

be an excisive triad with

nonempty, and suppose the pair

, and the pair

Then the map induced by the inclusion

A geometric proof is given in a book by Tammo tom Dieck.

[1] This result should also be seen as a consequence of the most general form of the Blakers–Massey theorem, which deals with the non-simply-connected case.

[2] The most important consequence is the Freudenthal suspension theorem.

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