RT Journal Article
T1 Realization of Permutation Modules via Alexandroff Spaces
A1 Costoya Ramos, María Cristina
A1 Gomes, Rafael
A1 Viruel Arbaizar, Antonio Ángel
K1 Permutation modules
K1 Automorphisms
K1 Graphs
K1 Posets
K1 Homotopy equivalences
AB We raise the question of the realizability of permutation mod ules in the context of Kahn’s realizability problem for abstract groups and the G-Moore space problem. Specifically, given a finite group G, we con sider a collection {Mi}ni=1 of finitely generated ZG-modules that admit asubmodule decomposition on which G acts by permuting the summands. Then we prove the existence of connected finite spaces X that realize each Mi as its i-th homology, G as its group of self-homotopy equiva lences E(X), and the action of G on each Mi as the action of E(X) onHi(X; Z)
PB Springer
SN 1422-6383
YR 2024
FD 2024-05-22
LK http://hdl.handle.net/10347/34927
UL http://hdl.handle.net/10347/34927
LA eng
NO Results Math 79, 169 (2024)
NO The first author was supported by MECIN/AEI/10.13039/501100011033 Grant PID2020-115155GB-I00. The second and third authors were supported by MECIN/AEI/10.13039/501100011033 Grant PID2020-118753GB-I00. The second author was also supported by Fundação para a Ciência e Tecnologia (Portugal) Grant 2021.04682.BD
DS Minerva
RD 28 abr 2026