Topological Hochschild homology of truncated Brown-Peterson spectra II

TL;DR

This paper computes the topological Hochschild homology of certain truncated Brown-Peterson spectra with new computational tools, revealing they are not Thom spectra at prime 2 for any n ≥ 2.

Contribution

It introduces a new variant of the Brun spectral sequence for computing topological Hochschild homology of truncated Brown-Peterson spectra.

Findings

Computed THH of $ ext{BP} extless n extgreater$ spectra at p=2

Developed a new computational spectral sequence tool

Showed these spectra are not Thom spectra at p=2 for n ≥ 2

Abstract

We compute topological Hochschild homology of $\mathbb{E}_3$-MU-algebra forms of the second truncated Brown-Peterson spectrum with Adams summand coefficients at $p=2$ and conditionally at arbitrary primes. We also provide a new computational tool, a variant of the Brun spectral sequence, for computing topological Hochschild homology of truncated Brown-Peterson spectra with certain coefficients. As a consequence, we show that $\mathbb{E}_3$-MU-algebra forms of truncated Brown-Peterson spectra are not Thom spectra $\mathrm{BP}\langle n\rangle$ at the prime $p=2$ for any $n\ge 2$.