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Representation Stability for Homotopy Groups of Configuration Spaces by Kupers, Alexander; Miller, Jeremy is a scholarly article available to read on EtoBox.

What is Representation Stability for Homotopy Groups of Configuration Spaces about?

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.

Author

Kupers, Alexander; Miller, Jeremy

Published

2014

Language

EN