Type 2 complexes constructed from Brown–Gitler spectra

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.