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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 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 †Σ m–polyhedral products, we give criteria on simplicial Σ m–complexes which imply representation stability of Σ m–representations {H i((X,A) Km)}

1472-2747
215-238
Fu, Xin
1190b059-0a15-4312-8321-86b04f82fd36
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
Fu, Xin
1190b059-0a15-4312-8321-86b04f82fd36
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175

Fu, Xin and Grbic, Jelena (2020) Simplicial G-complexes and representation stability of polyhedral products. Algebraic & Geometric Topology, 20 (1), 215-238. (doi:10.2140/agt.2020.20.215).

Record type: Article

Abstract

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 †Σ m–polyhedral products, we give criteria on simplicial Σ m–complexes which imply representation stability of Σ m–representations {H i((X,A) Km)}

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Accepted/In Press date: 24 February 2019
e-pub ahead of print date: 23 February 2020
Published date: 24 February 2020
Additional Information: Publisher Copyright: © 2020, Mathematical Sciences Publishers. All rights reserved.

Identifiers

Local EPrints ID: 429299
URI: http://eprints.soton.ac.uk/id/eprint/429299
ISSN: 1472-2747
PURE UUID: 47ebf3ad-9f46-410e-8060-d60932086136
ORCID for Jelena Grbic: ORCID iD orcid.org/0000-0002-7164-540X

Catalogue record

Date deposited: 26 Mar 2019 17:30
Last modified: 16 Mar 2024 04:13

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Contributors

Author: Xin Fu
Author: Jelena Grbic ORCID iD

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