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<p>In a previous paper, one of us interpreted mod 2 Dyer–Lashof operations as explicit <i>A</i>-module extensions between Brown–Gitler modules, and showed these <i>A</i>-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 <i>A</i>(1). Applications include classifying the dual Brown–Gitler spectra after localization with respect to <i>K</i>-theory.</p>

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Type 2 complexes constructed from Brown–Gitler spectra

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月26日

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  • William Balderrama,
  • Justin Barhite,
  • Nicholas J. Kuhn,
  • Donald M. Larson

摘要

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.