The Lubin–Tate theory of configuration spaces: I

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2024-10-20 DOI:10.1112/topo.70000

D. Lukas B. Brantner, Jeremy Hahn, Ben Knudsen

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引用次数: 0

Abstract

We construct a spectral sequence converging to the Lubin–Tate theory, that is, Morava $E$ -theory, of unordered configuration spaces and identify its $E^{2}$ -page as the homology of a Chevalley–Eilenberg-like complex for Hecke Lie algebras. Based on this, we compute the $E$ -theory of the weight $p$ summands of iterated loop spaces of spheres (parameterizing the weight $p$ operations on $E_{n}$ -algebras), as well as the $E$ -theory of the configuration spaces of $p$ points on a punctured surface. We read off the corresponding Morava $K$ -theory groups, which appear in a conjecture by Ravenel. Finally, we compute the $F_{p}$ -homology of the space of unordered configurations of $p$ particles on a punctured surface.

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构型空间的卢宾-塔特理论：I

我们构建了一个收敛于无序配置空间的卢宾-塔特理论（即莫拉瓦 E $E$ -理论）的谱序列，并将其 E 2 ${\mathrm{E}^2}$ -页确定为赫克李代数的切瓦利-艾伦伯格类复数的同调。在此基础上，我们计算了球面迭代环空间的权 p $p$ 和的 E $E$ 理论（参数化了 E n $\mathbb {E}_n$ -代数的权 p $p$ 运算），以及穿刺面上 p $p$ 点的配置空间的 E $E$ 理论。我们读出了相应的莫拉瓦 K $K$ 理论群，它们出现在拉文内尔的一个猜想中。最后，我们计算了穿刺面上 p $p$ 粒子无序配置空间的 F p $\mathbb {F}_p$ -同调。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.