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).

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 1999 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.