Universität zu Köln

Hausmann, Markus and Ostermayr, Dominik (2020). Filtrations of global equivariant K-theory. Math. Z., 295 (1-2). S. 161 - 211. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1823

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Abstract

Arone and Lesh (J Reine Angew Math 604:73-136, 2007; Fund Math 207(1):29-70, 2010) constructed and studied spectrum level filtrations that interpolate between connective (topological or algebraic) K-theory and the Eilenberg-MacLane spectrum for the integers. In this paper we consider (global) equivariant generalizations of these filtrations and another closely related class of filtrations, the modified rank filtrations of the K-theory spectra themselves. We lift Arone and Lesh's description of the filtration subquotients to the equivariant context and apply it to compute algebraic filtrations on representation rings that arise on equivariant homotopy groups. It turns out that these representation ring filtrations are considerably easier to express in a global equivariant context than over a fixed compact Lie group. Furthermore, they have formal similarities to the filtration on Burnside rings induced by the symmetric products of spheres, which was computed by Schwede (J Am Math Soc 30(3):673-711, 2017).

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Hausmann, Markus UNSPECIFIED UNSPECIFIED UNSPECIFIED Ostermayr, Dominik UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-332273
DOI:	10.1007/s00209-019-02338-1
Journal or Publication Title:	Math. Z.
Volume:	295
Number:	1-2
Page Range:	S. 161 - 211
Date:	2020
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-1823
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language RANK FILTRATION; HOMOTOPY-THEORY; SPECTRA; FUNCTORS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/33227