Hurewicz images of real bordism theory and real Johnson–Wilson theories
Hurewicz images of real bordism theory and real Johnson–Wilson theories
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DOI：
10.1016/j.aim.2018.11.002
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发表时间：
2017-07
影响因子：
1.7
通讯作者：
Guchuan Li;Xiaolin Shi;Guozhen Wang;Zhouli Xu
中科院分区：
文献类型：
--
作者：
Guchuan Li;Xiaolin Shi;Guozhen Wang;Zhouli Xu
我们表明，球体稳定同伦群中的 Hopf 元素、Kervaire 类和 κ 族可以通过 Hurewicz 图从球体谱到实数球谱的 C 2 不动点检测到。这些族的子集由 Real Johnson-Wilson 理论 E R (n) 的 C 2 不动点检测到，具体取决于 n。在证明中，我们建立了切片谱序列和B P R 的C 2 等变May谱序列之间的同构。
We show that the Hopf elements, the Kervaire classes, and the κ¯-family in the stable homotopy groups of spheres are detected by the Hurewicz map from the sphere spectrum to the C 2-fixed points of the Real bordism spectrum. A subset of these families is detected by the C 2-fixed points of Real Johnson–Wilson theory E R (n), depending on n. In the proof, we establish an isomorphism between the slice spectral sequence and the C 2-equivariant May spectral sequence of B P R.