On $BP⟨2⟩$-cooperations

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.

Fixed typos, slightly restructured paper, added section on structure theory of E(1)-modules, added details, streamlined some proofs. Submitted

References in corpus (2)

• Commutativity conditions for truncated Brown-Peterson spectra of height 2
• A Counterexample for Lightning Flash Modules over E(e1,e2)