词条 | Homotopy excision theorem |
释义 |
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. References1. ^T. tom Dieck, Algebraic Topology, EMS Textbooks in Mathematics, (2008). 2. ^R. Brown and J.-L. Loday, Homotopical excision and Hurewicz theorems for n-cubes of spaces, Proc. London Math. Soc., (3) 54 (1987) 176-192. Bibliography
2 : Homotopy theory|Theorems in algebraic topology |
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