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

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.

Minor changes, additional refrences. Final version, to appear in Journal of Homotopy and Related Structures

References in corpus (1)

• The Multiplication on BP