On Equivariant Maps Between Spheres with Involutions

P: w~nn 1 -* Z (see [7, p. 271] and [8, Th. A]), thereby verifying a conjecture of Bredon. In view of [8, Th. A], it only remains to improve a divisibility relation by a factor of 2 in case n _ 0(4), n > 0. However this is a delicate matter and is accomplished by means of Adams operations in equivariant KO-theory. The main theorem of [7] is a periodicity for the groups wn(r, q; t). A second aim of this note is to show that these groups may be viewed as cobordism groups, and that the periodicity then follows directly. This point of view also leads to an isomorphism of wn(r, q; t) with a suitable stable homotopy (or cohomotopy) group of a stunted real projective space. I would like to thank Professors M. Atiyah and G. Bredon for helpful conversations.