The ring of stable homotopy classes of self-maps of A(n,2)-polyhedra

David Méndez

Abstract:

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.

External IDs:doi:10.1016/j.topol.2021.107607