Homology, Homotopy and Applications

Volume 22 (2020)

Number 1

The Omega spectrum for Pengelley’s $BoP$

Pages: 11 – 25

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n1.a2


W. Stephen Wilson (Department of Mathematics, Johns Hopkins University, Baltimore, Maryland, U.S.A.)


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


homology, Hopf algebra, cobordism, homotopy type

2010 Mathematics Subject Classification

55N10, 55N22, 55P15

Received 27 January 2019

Accepted 12 April 2019

Published 18 September 2019