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2006 Completed representation ring spectra of nilpotent groups
Tyler Lawson
Algebr. Geom. Topol. 6(1): 253-285 (2006). DOI: 10.2140/agt.2006.6.253


In this paper, we examine the “derived completion” of the representation ring of a pro-p group Gp with respect to an augmentation ideal. This completion is no longer a ring: it is a spectrum with the structure of a module spectrum over the Eilenberg–MacLane spectrum , and can have higher homotopy information. In order to explain the origin of some of these higher homotopy classes, we define a deformation representation ring functor R[] from groups to ring spectra, and show that the map R[Gp]R[G] becomes an equivalence after completion when G is finitely generated nilpotent. As an application, we compute the derived completion of the representation ring of the simplest nontrivial case, the p–adic Heisenberg group.


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Tyler Lawson. "Completed representation ring spectra of nilpotent groups." Algebr. Geom. Topol. 6 (1) 253 - 285, 2006.


Received: 11 April 2005; Revised: 31 October 2005; Accepted: 5 January 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1118.55009
MathSciNet: MR2199460
Digital Object Identifier: 10.2140/agt.2006.6.253

Primary: 55P60
Secondary: 19A22, 55P43

Rights: Copyright © 2006 Mathematical Sciences Publishers


Vol.6 • No. 1 • 2006
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