Quillen homology of spectral Lie algebras with application to mod p homology of labeled configuration spaces
Year: 2025
Type: article
Abstract: We provide a general method computing the mod p Quillen homology of algebras over the monad that parametrizes the structure of mod p homology of spectral Lie algebras, including the construction of a May-type spectral sequence when p D 2. This is the E 2 -page of the bar spectral sequence converging to the mod p topological Quillen homology of spectral Lie algebras.As an application, we study the mod p homology of the labeled configuration space B k .M I X / of k points in a manifold M with labels in a spectrum X , which is the mod p topological Quillen homology of a certain spectral Lie algebra by a result of Knudsen.We obtain general upper bounds for the mod p homology of B k .M I X /, as well as explicit computations for k Ä 3. When p is odd, we observe that the mod p homology of B k .M n I S r / for small k depends only on the cohomology ring of the one-point compactification of M when n C r is even.This supplements and contrasts with the result of Bödigheimer, Cohen and Taylor when n C r is odd.
Source: Algebraic & Geometric Topology
Author: Adela YiYu Zhang
Institution: University of Copenhagen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4413378193