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Symmetric products and subgroup lattices

Markus Hausmann

Geometry & Topology 22 (2018) 1547–1591

Let G be a finite group. We show that the rational equivariant homotopy groups of symmetric products of the G–equivariant sphere spectrum are naturally isomorphic to the rational homology groups of certain subcomplexes of the subgroup lattice of G.

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symmetric products of spheres, global equivariant homotopy theory, subgroup lattices
Mathematical Subject Classification 2010
Primary: 55P42, 55P62, 55P91
Received: 27 July 2016
Revised: 4 June 2017
Accepted: 14 July 2017
Published: 16 March 2018
Proposed: Haynes R Miller
Seconded: Jesper Grodal, Peter Teichner
Markus Hausmann
Department of Mathematical Sciences
University of Copenhagen