Type 2 complexes constructed from Brown-Gitler spectra

TL;DR

This paper constructs and classifies type 2 complexes from Brown-Gitler spectra, revealing their chromatic properties and cohomology structure, and extends previous work on A-module extensions and topological realizations.

Contribution

It introduces new infinite families of type 2 spectra with free A(1)-cohomology and classifies dual Brown-Gitler spectra after K-theory localization.

Findings

Infinite families of type 2 spectra with free A(1)-cohomology

Construction of complexes from Brown-Gitler spectra as fibers of maps

Classification of dual Brown-Gitler spectra after K-theory localization

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.