Work

Type 2 complexes constructed from Brown–Gitler spectra

Year: 2025

Type: article

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.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-025-03869-6

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

Institutions: University of Bonn, University of Colorado Boulder, University of Virginia, Catholic University of America

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Rheinische Friedrich-Wilhelms-Universität Bonn