Filtered spectra arising from permutative categories : Journal für die reine und angewandte Mathematik (Crelles Journal) uses cookies, tags, and tracking settings to store information that help give you the very best browsing experience.
To understand more about cookies, tags, and tracking, see our Privacy Statement
I accept all cookies for the De Gruyter Online site

Jump to ContentJump to Main Navigation

Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

IMPACT FACTOR increased in 2014: 1.432
Rank 22 out of 310 in category Mathematics in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2014: 3.585
Source Normalized Impact per Paper (SNIP) 2014: 1.745
Impact per Publication (IPP) 2014: 1.262

Mathematical Citation Quotient (MCQ) 2014: 1.27



30,00 € / $42.00 / £23.00

Get Access to Full Text

Filtered spectra arising from permutative categories

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2007, Issue 604, Pages 73–136, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2007.020, June 2007

Publication History

Published Online:


Given a special Γ-category 𝒞 satisfying some mild hypotheses, we construct a sequence of spectra interpolating between the spectrum associated to 𝒞 and the Eilenberg-Mac Lane spectrum Hℤ. Examples of categories to which our construction applies are: the category of finite sets, the category of finite-dimensional vector spaces, and the category of finitely-generated free modules over a reasonable ring. In the case of finite sets, our construction recovers the filtration of Hℤ by symmetric powers of the sphere spectrum. In the case of finite-dimensional complex vector spaces, we obtain an apparently new sequence of spectra, {Am}, that interpolate between bu and . We think of Am as a “bu-analogue” of Spm(S) and describe far-reaching formal similarities between the two sequences of spectra. For instance, in both cases the mth subquotient is contractible unless m is a power of a prime, and in vk-periodic homotopy the filtration has only k + 2 non-trivial terms. There is an intriguing relationship between the bu-analogues of symmetric powers and Weiss's orthogonal calculus, parallel to the not yet completely understood relationship between the symmetric powers of spheres and the Goodwillie calculus of homotopy functors. We conjecture that the sequence {Am}, when rewritten in a suitable chain complex form, gives rise to a minimal projective resolution of the connected cover of bu. This conjecture is the bu-analogue of a theorem of Kuhn and Priddy about the symmetric power filtration. The calculus of functors provides substantial supporting evidence for the conjecture.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Gregory Z Arone, William G Dwyer, and Kathryn Lesh
Algebraic & Geometric Topology, 2008, Volume 8, Number 1, Page 173

Comments (0)

Please log in or register to comment.