Simplicial G–complexes and representation stability of polyhedral products

Fu, Xin¹ ; Grbić, Jelena¹

¹School of Mathematics, University of Southampton, Southampton, United Kingdom

Algebraic and Geometric Topology, Tome 20 (2020) no. 1, pp. 215-238

Résumé

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 G–complex K and a topological pair (X,A), a G–polyhedral product (X,A)K is associated. We show that the homotopy decomposition of Σ(X,A)K is then G–equivariant after suspension. In the case of Σm–polyhedral products, we give criteria on simplicial Σm–complexes which imply representation stability of Σm–representations {Hi((X,A)Km)}.

Détail

DOI : 10.2140/agt.2020.20.215

Classification : 20C30, 05E10, 55N91, 55U10
Keywords: polyhedral products, representation stability, symmetric groups

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