Cancellation and Non Cancellation Phenomena for Infinite Complexes

Let L(I, J) be defined by the pull-back of CPT >#(Q, 2)< QSJ where {/, /} is a partition of all primes. We classify spaces (Q Z* C(f)} of loop-suspension of mapping cone of phantom map f'.L(l, J) *S for k = 0, 1, , °° which have the same n-type for all n. In the category of finite CW-complexes, cancellation and non cancellation phenomena are well studied. In the category of infinite CW-complexes, the phenomena are less known. We study cancellation and non cancellation phenomena for infinite dimensional complexes by using above spaces.