The ring of stable homotopy classes of self-maps of A_n~2-polyhedra

摘要

We raise the problem of realisability of rings as {X, X} the ring of stable homotopy classes of self-maps of a space X. By focusing on A(n)(2)-polyhedra, we show that the direct sum of three endomorphism rings of abelian groups, one of which must be free, is realisable as {X, X} modulo the acyclic maps. We also show that F-p(3) is not realisable in the setting of finite type A(n)(2)-polyhedra, for p any prime. (C) 2021 Elsevier B.V. All rights reserved.