# Augmented Γ-spaces, the stable rank filtration, and a bu analogue of the Whitehead conjecture

Gregory Z. Arone; Kathryn Lesh

Fundamenta Mathematicae (2010)

- Volume: 207, Issue: 1, page 29-70
- ISSN: 0016-2736

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topGregory Z. Arone, and Kathryn Lesh. "Augmented Γ-spaces, the stable rank filtration, and a bu analogue of the Whitehead conjecture." Fundamenta Mathematicae 207.1 (2010): 29-70. <http://eudml.org/doc/282829>.

@article{GregoryZ2010,

abstract = {We explore connections between our previous paper [J. Reine Angew. Math. 604 (2007)], where we constructed spectra that interpolate between bu and Hℤ, and earlier work of Kuhn and Priddy on the Whitehead conjecture and of Rognes on the stable rank filtration in algebraic K-theory. We construct a "chain complex of spectra" that is a bu analogue of an auxiliary complex used by Kuhn-Priddy; we conjecture that this chain complex is "exact"; and we give some supporting evidence. We tie this to work of Rognes by showing that our auxiliary complex can be constructed in terms of the stable rank filtration. As a by-product, we verify for the case of topological complex K-theory a conjecture made by Rognes about the connectivity (for certain rings) of the filtration subquotients of the stable rank filtration of algebraic K-theory.},

author = {Gregory Z. Arone, Kathryn Lesh},

journal = {Fundamenta Mathematicae},

keywords = {Whitehead conjecture; Gamma spaces; calculus of functors; orthogonal calculus; rank filtration},

language = {eng},

number = {1},

pages = {29-70},

title = {Augmented Γ-spaces, the stable rank filtration, and a bu analogue of the Whitehead conjecture},

url = {http://eudml.org/doc/282829},

volume = {207},

year = {2010},

}

TY - JOUR

AU - Gregory Z. Arone

AU - Kathryn Lesh

TI - Augmented Γ-spaces, the stable rank filtration, and a bu analogue of the Whitehead conjecture

JO - Fundamenta Mathematicae

PY - 2010

VL - 207

IS - 1

SP - 29

EP - 70

AB - We explore connections between our previous paper [J. Reine Angew. Math. 604 (2007)], where we constructed spectra that interpolate between bu and Hℤ, and earlier work of Kuhn and Priddy on the Whitehead conjecture and of Rognes on the stable rank filtration in algebraic K-theory. We construct a "chain complex of spectra" that is a bu analogue of an auxiliary complex used by Kuhn-Priddy; we conjecture that this chain complex is "exact"; and we give some supporting evidence. We tie this to work of Rognes by showing that our auxiliary complex can be constructed in terms of the stable rank filtration. As a by-product, we verify for the case of topological complex K-theory a conjecture made by Rognes about the connectivity (for certain rings) of the filtration subquotients of the stable rank filtration of algebraic K-theory.

LA - eng

KW - Whitehead conjecture; Gamma spaces; calculus of functors; orthogonal calculus; rank filtration

UR - http://eudml.org/doc/282829

ER -

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