The Omega spectrum for Pengelley's BoP

TL;DR

This paper computes the homology and homotopy types of spaces in the Omega spectrum for BoP, providing complete results for indices up to 6 and conjectures beyond, advancing understanding of related spectra.

Contribution

It offers the first detailed homology and homotopy type computations for the Omega spectrum of BoP, extending known results and completing the homology of MSU spectra.

Findings

No torsion in homology for i ≥ 2

Complete homotopy types for i ≤ 6

Conjectured homotopy types for i > 6

Abstract

We compute the homology of the spaces in the Omega spectrum for $BoP$. There is no torsion in $H_*(\underline{BoP}_{\; i})$ for $i \ge 2$, and things are only slightly more complicated for $i < 2$. We find the complete homotopy type of $\underline{BoP}_{\; i}$ for $i \le 6$ and conjecture the homotopy type for $i > 6$. This completes the computation of all $H_*(\underline{MSU}_{\;*})$.