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Simplicial G-complexes and representation stability of polyhedral products

Simplicial G-complexes and representation stability of polyhedral products
Simplicial G-complexes and representation stability of polyhedral products
Representation stability in the sense of Church-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~\cite{BBCG} of $\Sigma (X, A)^K$ is then $G$-equivariant after suspension.
In the case of $\Sigma_m$-polyhedral products, we give criteria on simplicial $\Sigma_m$-complexes which imply representation stability of $\Sigma_m$-representations $\{H_i((X, A)^{K_m})\}$.
1472-2747
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Fu, Xin
1190b059-0a15-4312-8321-86b04f82fd36
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Fu, Xin
1190b059-0a15-4312-8321-86b04f82fd36

Grbic, Jelena and Fu, Xin (2019) Simplicial G-complexes and representation stability of polyhedral products. Algebraic & Geometric Topology. (In Press)

Record type: Article

Abstract

Representation stability in the sense of Church-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~\cite{BBCG} of $\Sigma (X, A)^K$ is then $G$-equivariant after suspension.
In the case of $\Sigma_m$-polyhedral products, we give criteria on simplicial $\Sigma_m$-complexes which imply representation stability of $\Sigma_m$-representations $\{H_i((X, A)^{K_m})\}$.

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FuGrbic_RSPPv2 - Accepted Manuscript
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Accepted/In Press date: 24 February 2019

Identifiers

Local EPrints ID: 429299
URI: https://eprints.soton.ac.uk/id/eprint/429299
ISSN: 1472-2747
PURE UUID: 47ebf3ad-9f46-410e-8060-d60932086136

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Date deposited: 26 Mar 2019 17:30
Last modified: 25 Apr 2019 04:01

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