On the -cohomology of rings of numerical polynomials and E∞ structures on K-theory
On the -cohomology of rings of numerical polynomials and E∞ structures on K-theory
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K理论上数值多项式环与E∞结构的-上同调
DOI：
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发表时间：
2005
期刊：
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通讯作者：
Birgit Richter
中科院分区：
文献类型：
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作者：
Andrew H. Baker;Birgit Richter
利用周期上同调理论研究了交换合作代数E <$E的上同调.对于KU和E（1），亚当斯和项在素数p处，对于KO，我们证明了在1次以上β-上同调为零。由于这些相干群是Alan罗宾逊发展的阻塞理论中的阻塞群，我们推断这些谱具有唯一的E∞结构。作为结果，我们得到了E∞结构的连接亚当斯和。对于Johnson-Wilson谱E（n）（n = 1），我们证明了它的In-adic完备化存在唯一的E∞结构.
We investigate � -cohomology of some commutative cooperation algebras E∗E as- sociated with certain periodic cohomology theories. For KU and E(1), the Adams summand at a prime p, and for KO we show that � -cohomology vanishes above degree 1. As these cohom- ology groups are the obstruction groups in the obstruction theory developed by Alan Robinson we deduce that these spectra admit unique E∞ structures. As a consequence we obtain an E∞ structure for the connective Adams summand. For the Johnson-Wilson spectrum E(n) with n 1 we establish the existence of a unique E∞ structure for its In-adic completion.