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

• Autorzy: Gregory Z. Arone , Kathryn Lesh
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 55R45: Homology and homotopy of B O and B U ; Bott periodicity
• 55P91: Equivariant homotopy theory
• 19L41: Connective K -theory, cobordism
• 55P48: Loop space machines, operads

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 207
• Numer: 1
• Strony: 29-70

Daty

wydano

2010

Twórcy

autor

Gregory Z. Arone

• Kerchof Hall, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904, U.S.A.

autor

Kathryn Lesh

• Department of Mathematics, Union College, Schenectady, NY 12309, U.S.A.

Identyfikatory

DOI

10.4064/fm207-1-3