Manifolds with involution whose fixed point set \(F\) has the property \(W(F)=1\) (Q1178397)

This paper attempts to determine the possible cobordism classes of involutions for which the fixed set has trivial Stiefel-Whitney class. Unfortunately, the proof is completely inadequate. The main technical points needed are given in Lemma 1 and the assertions made there all require verification. The classes \(A\) used are elements of the bordism ring, and are not easily seen to be in \(\mathbb{Z}/2\mathbb{Z}\). The equation derived from that only holds up to bordism and it is far from clear that the integers \(i\) must be of the form \(2^ s-1\). Finally, it appears that Lemma 1 needs to be strengthened in order to apply in the proof of the Theorem --- more than one s-number may be nonzero, and one must consider sums of classes.