Homotopy excision theorem: Difference between revisions

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is bijective for <math>q < m+n-2</math> and is surjective for <math>q = m+n-2</math>.

A nice geometric proof is given in the book by tom Dieck. <ref>T. tom Dieck, ''Algebraic Topology'', EMS Textbooks in Mathematics, (2008).</ref>

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.<ref>R. Brown and J.-L. Loday, is''Homotopical inexcision theand paperHurewicz theorems for ''n''-cubes of Brownspaces'', andProc. LodayLondon referencedMath. belowSoc., (3) 54 (1987) 176-192.</ref>

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

== References ==

{{reflist}}

* J.P. May, ''A Concise Course in Algebraic Topology'', Chicago University Press.

== Bibliography ==

* T. tom Dieck, ''Algebraic Topology'', EMS Textbooks in Mathematics, (2008).

* J.P. May, ''A Concise Course in Algebraic Topology'', Chicago University Press.

* 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.

[[Category:Homotopy theory]]