The smooth Whitehead spectrum of a point at odd regular primes
The smooth Whitehead spectrum of a point at odd regular primes
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奇数正则素数点的平滑怀特海谱
DOI：
10.2140/gt.2003.7.155
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发表时间：
2003
影响因子：
2
通讯作者：
J. Rognes
中科院分区：
文献类型：
--
作者：
J. Rognes
令 p 为奇正则素数，并假设 Lichtenbaum{Quillen 猜想对于 p 处的 K(Z[1=p]) 成立。然后描述了平滑Whitehead谱Wh()的p主同伦型。 J 谱的 cokernel 的悬浮副本分裂 o，并且其余部分的扭转同伦等于受限 S 1 -传递图 t 的 ber 的扭转同伦：C P 1 ！ S. Wh () 的同伦群在一定度数范围内确定，并且 Wh () 的上同调表示为所有度数的 A 模，直至扩展。这些结果具有几何拓扑解释，即高度连通、高维紧致光滑流形的一致性空间或异态。
Let p be an odd regular prime, and assume that the Lichtenbaum{Quillen conjecture holds for K(Z[1=p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh () is described. A suspended copy of the cokernel-of-J spectrum splits o, and the torsion homotopy of the remainder equals the torsion homotopy of the ber of the restricted S 1 -transfer map t : C P 1 ! S. The homotopy groups of Wh () are determined in a range of degrees, and the cohomology of Wh () is expressed as an A-module in all degrees, up to an extension. These results have geometric topological interpretations, in terms of spaces of concordances or dieomorphisms of highly connected, high dimensional compact smooth manifolds.