Volume 20, issue 1 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20, 1 issue

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

Author Index
The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
Other MSP Journals
Simplicial $G$–complexes and representation stability of polyhedral products

Xin Fu and Jelena Grbić

Algebraic & Geometric Topology 20 (2020) 215–238

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)}.

polyhedral products, representation stability, symmetric groups
Mathematical Subject Classification 2010
Primary: 20C30
Secondary: 05E10, 55N91, 55U10
Received: 5 March 2018
Revised: 17 November 2018
Accepted: 24 February 2019
Published: 23 February 2020
Xin Fu
School of Mathematics
University of Southampton
United Kingdom
Jelena Grbić
School of Mathematics
University of Southampton
United Kingdom