The Lubin-Tate Theory of Configuration Spaces: I

2019/08/29 by Lukas Brantner, Jeremy Hahn, Brantner, Lukas +3
Mathematics · #17B56 #55N15 #55N20 #55P35 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1908.11321

openalex publication_date 2019/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a spectral sequence converging to the Morava E-theory of unordered configuration spaces and identify its E²-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 (parametrising 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 \mathbbF_p-homology of the space of unordered configurations of p particles on a punctured surface.

Citations

• The Morava E-theories of finite general linear groups
• The mod 2 homology of free spectral Lie algebras

Related

• The Morava E-theory of Eilenberg-Mac Lane spaces
• Lubin-Tate theory, character theory, and power operations
• Configuration spaces on the sphere and higher loop spaces
• Lie algebras and the (co)homology of configuration spaces
• Mod p homology of unordered configuration spaces of surfaces