Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

A conjecture on the unstable Adams spectral sequences for SO and U

100%

Lesh K.

Fundamenta Mathematicae

2002

tom 174

nr 1

49-78

We give a systematic account of a conjecture suggested by Mark Mahowald on the unstable Adams spectral sequences for the groups SO and U. The conjecture is related to a conjecture of Bousfield on a splitting of the E₂-term and to an algebraic spectral sequence constructed by Bousfield and Davis. We construct and realize topologically a chain complex which is conjectured to contain in its differential the structure of the unstable Adams spectral sequence for SO. A filtration of this chain complex gives rise to a spectral sequence that is conjectured to be the unstable Adams spectral sequence for SO. If the conjecture is correct, then it means that the entire unstable Adams spectral sequence for SO is available from a primary level calculation. We predict the unstable Adams filtration of the homotopy elements of SO based on the conjecture, and we give an example of how the chain complex predicts the differentials of the unstable Adams spectral sequence. Our results are also applicable to the analogous situation for the group U.

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

63%

Arone G., Lesh K.

Fundamenta Mathematicae

2010

tom 207

nr 1

29-70

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.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Lesh K.

1 Arone G.

1 2010

1 2002

Wyniki wyszukiwania

A conjecture on the unstable Adams spectral sequences for SO and U

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