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Real topological Hochschild homology and the Segal conjecture
Advances in Mathematics ( IF 1.5 ) Pub Date : 2021-06-15 , DOI: 10.1016/j.aim.2021.107839
Jeremy Hahn , Dylan Wilson

We give a new proof, independent of Lin's theorem, of the Segal conjecture for the cyclic group of order two. The key input is a calculation, as a Hopf algebroid, of the Real topological Hochschild homology of F2. This determines the E2-page of the descent spectral sequence for the map NF2F2, where NF2 is the C2-equivariant Hill–Hopkins–Ravenel norm of F2. The E2-page represents a new upper bound on the RO(C2)-graded homotopy of NF2, from which the Segal conjecture is an immediate corollary.



中文翻译:

实拓扑霍克希尔德同调和西格尔猜想

我们对二阶循环群的 Segal 猜想给出了独立于 Lin 定理的新证明。关键输入是作为 Hopf 代数计算的实拓扑 Hochschild 同调F2. 这决定了2- 地图的下降谱序列的页面 NF2F2, 在哪里 NF2 是个 C2的等变 Hill–Hopkins–Ravenel 范数 F2. 这2-page 表示新的上限 电阻(C2)- 分级同伦 NF2,由此西格尔猜想是直接推论。

更新日期:2021-06-15
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