增广Gamma空间、稳定秩滤子和Whitehead猜想的Bu-模拟
Augmented Gamma-spaces, the stable rank filtration, and a bu-analogue of the Whitehead Conjecture
摘要：
我们探讨我们早期的工作，我们在其中构建的频谱之间的插值BU和HZ，和早期的工作库恩和Priddy的怀特黑德猜想和Rognes的稳定秩过滤在代数K理论。我们构建了一个“链复形的光谱”，这是一个bu-analogue的辅助复杂的库恩-Priddy，我们猜想，这链复形是“精确的”，我们给出了一些支持的证据。我们把这一工作的Rognes表明，我们的辅助复合物可以构建在稳定的秩过滤。作为一个副产品，我们验证的情况下，拓扑复杂的K-理论的一个猜想，由Rognes的连通性（某些环）的过滤subconformants的稳定秩过滤的代数K理论。
英文摘要：
We explore connections between our earlier work, in which 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.
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