On conjectures of Mahowald, Segal and Sullivan

Abstract

In this paper we prove some results about the stable homotopy and cohomotopy of spaces related to the infinite real protective space RP∞. These include M. E. Mahowald's conjecture on the limit of stable homotopy of stunted real projective spaces RP2N+m/RP2N−m as N, m → ∞, G. Segal's Burnside ring conjecture forand the stable analogue of a conjecture of D. Sullivan on RP∞.