On BP⟨2⟩–cooperations

Culver, Dominic

doi:10.2140/agt.2019.19.807

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

Dominic Leon Culver

Algebraic & Geometric Topology 19 (2019) 807–862

DOI: 10.2140/agt.2019.19.807

Abstract

We develop techniques to compute the cooperations algebra for the second truncated Brown–Peterson spectrum $BP 〈 2 〉$ . We prove that the cooperations algebra $BP {〈 2 〉}_{*} BP 〈 2 〉$ decomposes as a direct sum of an $F_{2}$ –vector space concentrated in Adams filtration $0$ and an $F_{2} [v_{0}, v_{1}, v_{2}]$ –module which is concentrated in even degrees and is $v_{2}$ –torsion-free. We also develop a recursive method which produces a basis for the $v_{2}$ –torsion-free component.

Keywords

cooperations, Brown–Peterson spectrum, Adams spectral sequence, Brown–Gitler modules

Mathematical Subject Classification 2010

Primary: 55S10, 55S99, 55T15

References

Publication

Received: 22 September 2017

Revised: 14 August 2018

Accepted: 17 September 2018

Published: 12 March 2019

Authors

Dominic Leon Culver
Department of Mathematics University of Illinois, Urbana-Champaign Urbana, IL United States

Volume 19, issue 2 (2019)