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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