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arXiv · 2409.16384

Type 2 complexes constructed from Brown-Gitler spectra

William Balderrama·Justin Barhite·Nicholas J. Kuhn·Donald M. Larson
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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.

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William Balderrama, Justin Barhite, Nicholas J. Kuhn, Donald M. Larson. 2024-09-24. Type 2 complexes constructed from Brown-Gitler spectra. https://arxiv.org/abs/2409.16384

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