Volume 19, issue 2 (2019)

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On $\mathrm{BP}\langle 2\rangle$–cooperations

Dominic Leon Culver

Algebraic & Geometric Topology 19 (2019) 807–862

We develop techniques to compute the cooperations algebra for the second truncated Brown–Peterson spectrum BP2. We prove that the cooperations algebra BP2BP2 decomposes as a direct sum of an F2–vector space concentrated in Adams filtration 0 and an F2[v0,v1,v2]–module which is concentrated in even degrees and is v2–torsion-free. We also develop a recursive method which produces a basis for the v2–torsion-free component.

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cooperations, Brown–Peterson spectrum, Adams spectral sequence, Brown–Gitler modules
Mathematical Subject Classification 2010
Primary: 55S10, 55S99, 55T15
Received: 22 September 2017
Revised: 14 August 2018
Accepted: 17 September 2018
Published: 12 March 2019
Dominic Leon Culver
Department of Mathematics
University of Illinois, Urbana-Champaign
Urbana, IL
United States