2019/08/24 by Xianglong Ni, Ni, Xianglong
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1908.09233
openalex publication_date 2019/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When X is an associative H-space, the bar spectral sequence computes the homology of the delooping, H*(BX). If X is an n-fold loop space for n≥2 this is a spectral sequence of Hopf algebras. Using machinery by Sugawara and Clark, we show that the spectral sequence filtration respects the Browder bracket structure on H*(BX), and so it is moreover a spectral sequence of Poisson algebras. Through the bracket on the spectral sequence, we establish a connection between the degree n-1 bracket on H*(X) and the degree n-2 bracket on H*(BX). This generalizes a result of Browder and puts it in a computational context.