On the Hopf ring for ER(n)
On the Hopf ring for ER(n)
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在 ER(n) 的 Hopf 环上
DOI：
10.1016/j.topol.2007.01.001
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发表时间：
2007
影响因子：
0.6
通讯作者：
−→ H∗En
中科院分区：
文献类型：
--
作者：
N. Kitchloo;Stephen M. J. Wilson;−→ H∗En
Kriz和Hu构造了实约翰逊-威尔逊谱ER(N)，它是2n+2(2n−1)周期的。Er(1)就是KO(2)。在这篇论文中，我们做了两件事。首先，我们计算了ER(N)的欧米伽谱中2n个−1空间的同调。证明了这些Hopf代数的对偶给出了E(N)的偶空间的同调Hopf代数。作为一个副产品，我们得到了实复余边同调和实Brown-Peterson上同调的Omega谱的第零空间的同调。第二个结果是计算了ER(2)的Omega谱中所有48个空间的同调Hopf环。事实证明，这是由很少的元素产生的。
Kriz and Hu construct a real Johnson–Wilson spectrum, ER(n), which is 2n+2(2n−1) periodic. ER(1) is just KO(2). We do two things in this paper. First, we compute the homology of the 2n−1 spaces [Formula: see text] in the Omega spectrum for ER(n). It turns out the double of these Hopf algebras gives the homology Hopf algebras for the even spaces for E(n). As a byproduct of this we get the homology of the zeroth spaces for the Omega spectrum for real complex cobordism and real Brown–Peterson cohomology. The second result is to compute the homology Hopf ring for all 48 spaces in the Omega spectrum for ER(2). This turns out to be generated by very few elements.