Correction to my paper, “on $\langle 8 \rangle$-cobordism”

Abstract

the proof of Theorem 3.3 is incorrect.The statement of the theorem, nd the outline of a correct proof are given below.THEOREM3.3.(i) d,(r) hco, (ii) dr(x) 0 for all r.(iii) da(eo) coco.Proof. (i) The sequence &() h0 do.m(BO) J ,r,(S) --* f<> --> m(BO) is exact, and J is the ordinary J homomorphism.Hence 2< > 0, so &.(r) h co.The second part of 1 follows from h0 h r.(ii) By computing the relative group ''" one shows that <> Z.Since there is only one infinite cycle in dimension 15, [hi ], all the elements in dimension 16 must be infinite cycles, so (ii) follows.(iii) It can be shown by a homotopy argument that coco cannot live to E. It must be a cycle, hence also a boundary.Thus da(eo) coCo.