Homotopy classification of maps between r−1 connected 2r dimensional manifolds

Abstract

In this paper, we study the homotopy classification of continuous maps between two r−1 connected 2r dimensional topological manifolds M, N. If we assume some knowledge on the homotopy groups of spheres, then the complete classification can be obtained from the homotopy invariants of M, N. We design an algorithm and compose a program to give explicit computations.