$BP$: Close encounters of the $E_\infty$ kind

Andrew Baker

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arXiv · 1204.4878

$BP$: Close encounters of the $E_\infty$ kind

Andrew Baker

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Abstract

Inspired by Stewart Priddy's cellular model for the $p$-local Brown-Peterson spectrum $BP$, we give a construction of a $p$-local $E_\infty$ ring spectrum $R$ which is a close approximation to $BP$. Indeed we can show that if $BP$ admits an $E_\infty$ structure then these are weakly equivalent as $E_\infty$ ring spectra. Our inductive cellular construction makes use of power operations on homotopy groups to define homotopy classes which are then killed by attaching $E_\infty$ cells.

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Andrew Baker. 2013-07-29. $BP$: Close encounters of the $E_\infty$ kind. https://arxiv.org/abs/1204.4878

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