Geometry & Topology

The character of the total power operation

Tobias Barthel and Nathaniel Stapleton

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Abstract

We compute the total power operation for the Morava E–theory of any finite group up to torsion. Our formula is stated in terms of the GLn(p)–action on the Drinfel’d ring of full level structures on the formal group associated to E–theory. It can be specialized to give explicit descriptions of many classical operations. Moreover, we show that the character map of Hopkins, Kuhn and Ravenel from E–theory to GLn(p)–invariant generalized class functions is a natural transformation of global power functors on finite groups.

Article information

Source
Geom. Topol., Volume 21, Number 1 (2017), 385-440.

Dates
Received: 26 February 2015
Revised: 26 September 2016
Accepted: 15 January 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510859137

Digital Object Identifier
doi:10.2140/gt.2017.21.385

Mathematical Reviews number (MathSciNet)
MR3608717

Zentralblatt MATH identifier
1360.55004

Subjects
Primary: 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] 55S25: $K$-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]
Secondary: 55P42: Stable homotopy theory, spectra

Keywords
power operations generalized character theory Morava $E$–theory

Citation

Barthel, Tobias; Stapleton, Nathaniel. The character of the total power operation. Geom. Topol. 21 (2017), no. 1, 385--440. doi:10.2140/gt.2017.21.385. https://projecteuclid.org/euclid.gt/1510859137


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