HOMOTOPY CLASSIFICATION OF MAPS BETWEEN PSEUDO-PROJECTIVE PLANES

Abstract

The pseudo-projective plane M(q) is obtained by attaching a two cell to a circle by a map of degree q. We here determine the homotopy classes (M(q), M(w)) and some of their properties in the unbased, based and cellular-preserving cases. In the cellular-preserving case the sets have a near-ring structure for q = w but the addition is lost on passing to the based case. The results, known for q = w = 2, are compared to the known result for ϵ(M(q)) the group of based self-homotopy equivalence classes.