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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
中文翻译:
实拓扑霍克希尔德同调和西格尔猜想
更新日期:2021-06-15
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 . This determines the -page of the descent spectral sequence for the map , where is the -equivariant Hill–Hopkins–Ravenel norm of . The -page represents a new upper bound on the -graded homotopy of , 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. 这决定了- 地图的下降谱序列的页面 , 在哪里 是个 的等变 Hill–Hopkins–Ravenel 范数 . 这-page 表示新的上限 - 分级同伦 ,由此西格尔猜想是直接推论。