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arXiv · 1708.03001

On $BP\langle 2\rangle$-cooperations

Dominic Culver
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Abstract

In this paper we develop techniques to compute the cooperations algebra for the second truncated Brown-Peterson spectrum $\tBP{2}$. We prove that the cooperations algebra $\tBP{2}_*\tBP{2}$ decomposes as a direct some of a $\F_2$-vector space concentrated in Adams filtration 0 and a $\F_2[v_0,v_1,v_2]$-module which is concentrated in even degrees and $v_2$-torsion free. A recursive procedure is also developed to provide an basis of the $v_2$-torsion free part.

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Dominic Culver. 2017-08-09. On $BP\langle 2\rangle$-cooperations. https://doi.org/10.2140/agt.2019.19.807

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