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)}
215-238
Fu, Xin
1190b059-0a15-4312-8321-86b04f82fd36
Grbic, Jelena
daaea124-d4cc-4818-803a-2b0cb4362175
24 February 2020
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), .
(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 †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)}
Text
FuGrbic_RSPPv2
- Accepted Manuscript
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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
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© 2020, Mathematical Sciences Publishers. All rights reserved.
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Local EPrints ID: 429299
URI: http://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: 06 Jun 2024 01:51
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Author:
Xin Fu
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