Representation stability in the sense of Church and Farb is concerned with stable properties of representations of sequences of algebraic structures, in particular of groups. We study this notion on objects arising in toric topology. With a simplicial –complex and a topological pair , a –polyhedral product is associated. We show that the homotopy decomposition of is then –equivariant after suspension. In the case of –polyhedral products, we give criteria on simplicial –complexes which imply representation stability of –representations .
"Simplicial –complexes and representation stability of polyhedral products." Algebr. Geom. Topol. 20 (1) 215 - 238, 2020. https://doi.org/10.2140/agt.2020.20.215