Type 2 complexes constructed from Brown-Gitler spectra
Algebraic Topology
2025-07-30 v3
Abstract
In a previous paper, one of us interpreted mod 2 Dyer-Lashof operations as explicit A-module extensions between Brown-Gitler modules, and showed these A-modules can be topologically realized by finite spectra occurring as fibers of maps between 2-local dual Brown-Gitler spectra. Starting from these constructions, in this paper, we show that infinite families of these finite spectra are of chromatic type 2, with mod 2 cohomology that is free over A(1). Applications include classifying the dual Brown-Gitler spectra after localization with respect to K-theory.
Cite
@article{arxiv.2409.16384,
title = {Type 2 complexes constructed from Brown-Gitler spectra},
author = {William Balderrama and Justin Barhite and Nicholas J. Kuhn and Donald M. Larson},
journal= {arXiv preprint arXiv:2409.16384},
year = {2025}
}
Comments
28 pages. v2: minor revisions, with a much improved formulation of the main theorem. v3: two new figures; accepted version, to appear in Mathematische Zeitschrift