Geometry & Topology

Symmetric products and subgroup lattices

Markus Hausmann

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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 .

Article information

Geom. Topol., Volume 22, Number 3 (2018), 1547-1591.

Received: 27 July 2016
Revised: 4 June 2017
Accepted: 14 July 2017
First available in Project Euclid: 31 March 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P42: Stable homotopy theory, spectra 55P62: Rational homotopy theory 55P91: Equivariant homotopy theory [See also 19L47]

symmetric products of spheres global equivariant homotopy theory subgroup lattices


Hausmann, Markus. Symmetric products and subgroup lattices. Geom. Topol. 22 (2018), no. 3, 1547--1591. doi:10.2140/gt.2018.22.1547.

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