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

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

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.

A -polyhedra, Stable self-homotopy equivalences
0166-8641
Méndez, David
082b86ce-ba78-4519-9713-ff1a38f65c96
Méndez, David
082b86ce-ba78-4519-9713-ff1a38f65c96

Méndez, David (2021) The ring of stable homotopy classes of self-maps of A(n,2)-polyhedra. Topology and its Applications, 290, [107607]. (doi:10.1016/j.topol.2021.107607).

Record type: Article

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.

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Ring_of_endomorphisms - Accepted Manuscript
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Accepted/In Press date: 10 January 2021
e-pub ahead of print date: 12 January 2021
Published date: 1 March 2021
Additional Information: Publisher Copyright: © 2021 Elsevier B.V.
Keywords: A -polyhedra, Stable self-homotopy equivalences

Identifiers

Local EPrints ID: 446449
URI: http://eprints.soton.ac.uk/id/eprint/446449
DOI: doi:10.1016/j.topol.2021.107607
ISSN: 0166-8641
PURE UUID: 8cb656a7-9cc7-4525-95bf-4b6b4c26ca13
ORCID for David Méndez: ORCID iD orcid.org/0000-0003-4023-172X

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Date deposited: 10 Feb 2021 17:33
Last modified: 17 Mar 2024 06:14

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Author: David Méndez ORCID iD

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