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arXiv · 2105.11325

Representation stability for homotopy automorphisms

Erik Lindell·Bashar Saleh
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Abstract

We consider in parallel pointed homotopy automorphisms of iterated wedge sums of topological spaces 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.

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Erik Lindell, Bashar Saleh. 2021-05-24. Representation stability for homotopy automorphisms. https://doi.org/10.2140/agt.2024.24.2673

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