Loop space homology associated to the mod 2 Dickson invariants

2010/01/20 by Ran Levi, Levi, Ran, Nora Seeliger +1
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1001.3581

openalex publication_date 2010/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The spaces BG₂ and BDI(4) have the property that their mod 2 cohomology is given by the rank 3 and 4 Dickson invariants respectively. Associated with these spaces one has for q odd the classifying spaces of the finite groups BG₂(q)and the exotic family of classifying spaces of 2-local finite groups BSol(q). In this article compute the mod 2 loop space homology of the 2-completed classifying space of G₂(q) and of BSol(q) for all odd primes q, as algebras over the Steenrod algebra, and the associated Bockstein spectral sequences.

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