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 nice geometric proof is given in the book by tom Dieck.[1]
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.[2]
The most important consequence is the Freudenthal suspension theorem.
References
Bibliography
- J.P. May, A Concise Course in Algebraic Topology, Chicago University Press.
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