Representation stability for homotopy groups of configuration spaces

Alexander Kupers; Jeremy Miller

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arXiv · 1410.2328

Representation stability for homotopy groups of configuration spaces

Alexander Kupers·Jeremy Miller

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Abstract

We prove that the dual rational homotopy groups of the configuration spaces of a 1-connected manifold of dimension at least 3 are uniformly representation stable in the sense of Church, and that their derived dual integral homotopy groups are finitely-generated as FI-modules in the sense of Church-Ellenberg-Farb. This is a consequence of a more general theorem relating properties of the cohomology groups of a 1-connected co-FI-space to properties of its dual homotopy groups. We also discuss several other applications.

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Alexander Kupers, Jeremy Miller. 2015-04-28. Representation stability for homotopy groups of configuration spaces. https://arxiv.org/abs/1410.2328

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