Representation stability for homotopy automorphisms

Lindell, Erik; Saleh, Bashar

doi:10.2140/agt.2024.24.2673

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Representation stability for homotopy automorphisms

Erik Lindell and Bashar Saleh

Algebraic & Geometric Topology 24 (2024) 2673–2705

DOI: 10.2140/agt.2024.24.2673

Abstract

We consider in parallel pointed homotopy automorphisms of iterated wedge sums of finite CW–complexes and boundary-relative homotopy automorphisms of iterated connected sums of manifolds minus a disk. Under certain conditions on the spaces and manifolds, we prove that the rational homotopy groups of these homotopy automorphisms form finitely generated $FI$ –modules, and thus satisfy representation stability for symmetric groups in the sense of Church and Farb. We also calculate explicit bounds on the weights and stability degrees of these $FI$ –modules.

Keywords

representation stability, homotopy automorphisms

Mathematical Subject Classification

Primary: 55P62

References

Publication

Received: 7 June 2022

Revised: 17 July 2023

Accepted: 20 August 2023

Published: 19 August 2024

Authors

Erik Lindell
Department of Mathematical Sciences University of Copenhagen Copenhagen Denmark

Bashar Saleh
Department of Mathematics Stockholm University Stockholm Sweden

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Volume 24, issue 5 (2024)