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 E k F P m of a projective space F P m and Y is a sphere S n or F P n for F = R , C , the fields of real or complex numbers, respectively. In particular, the cohomotopy sets π n ( E k F P m ) are studied for k ≥ 0 and certain m , n ≥ 1 .

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