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2020 Simplicial G–complexes and representation stability of polyhedral products
Xin Fu, Jelena Grbić
Algebr. Geom. Topol. 20(1): 215-238 (2020). DOI: 10.2140/agt.2020.20.215

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 Σm–polyhedral products, we give criteria on simplicial Σm–complexes which imply representation stability of Σm–representations {Hi((X,A)Km)}.

Citation

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Xin Fu. Jelena Grbić. "Simplicial G–complexes and representation stability of polyhedral products." Algebr. Geom. Topol. 20 (1) 215 - 238, 2020. https://doi.org/10.2140/agt.2020.20.215

Information

Received: 5 March 2018; Revised: 17 November 2018; Accepted: 24 February 2019; Published: 2020
First available in Project Euclid: 19 July 2021

Digital Object Identifier: 10.2140/agt.2020.20.215

Subjects:
Primary: 20C30
Secondary: 05E10, 55N91, 55U10

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 1 • 2020
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