0. BASIC HOMOTOPY NOTIONS 7 one on each M(a) in the following way: Let [M] G Hm(\M\,d\M\) be the fundamental class. Let A|M| = U {M(a) :\a\^n- 2}. Then the image of [M] under Hm(\M\,d\M\) h Hm^{d\M\) h Hm-^dlMl A\M\) = 0 Hrn^1(\diMld\diM\) (where j * is the inclusion map) shall be denoted by E i K n ( ~ ^ ) 1 ^ ^ ] ' Now by induction we obtain fundamental classes for each M(a)\ the usual combinatorial argument which shows that d2 = 0 in a simplicial complex demonstrates that the class so obtained depends only on a (and not on any choice of construction).
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