Homotopy excision theorem
Appearance
In algebraic topology, the homotopy excision theorem offers a substitute for the absence of excision in homotopy theory. More precisely, let X be a space that is union of the interiors of subspaces A, B with nonempty, and suppose a pair is ()-connected, , and a pair is ()-connected, . Then, for the inclusion ,
is bijective for and is surjective for .
The most important consequence is the Freudenthal suspension theorem.
References
- J.P. May, A Concise Course in Algebraic Topology, Chicago University Press