Homotopies of maps of suspended real and complex projective spaces and their cohomotopy groups

Abstract

We describe the set [X,Y] of path-components of pointed mapping spaces M⁎(X,Y), where X is chosen to be the reduced kth suspension EkFPm of a projective space FPm and Y is a sphere Sn or FPn for F=R,C, the fields of real or complex numbers, respectively. In particular, the cohomotopy sets πn(EkFPm) are studied for k≥0 and certain m,n≥1.