On a Spectrum-level Splitting of the $BP \langle 2 \rangle$-Cooperations Algebra

Elizabeth Ellen Tatum

On a Spectrum-level Splitting of the $BP \langle 2 \rangle$-Cooperations Algebra

Algebraic Topology 2023-03-10 v2

Authors: Elizabeth Ellen Tatum

Abstract

In the 1980s, Mahowald and Kane used Brown-Gitler spectra to construct splittings of $bo \wedge bo$ and $BP\langle 1 \rangle \wedge BP\langle 1 \rangle$ . These splittings helped make it feasible to do computations using the $bo$ - and $BP \langle 1 \rangle$ -based Adams spectral sequences. In this paper, we construct an analogous splitting for $BP \langle 2 \rangle \wedge BP\langle 2 \rangle$ .

Keywords

brown-gitler spectra bo bp<2> adams spectral sequence spectrum splitting

Cite

@article{arxiv.2208.11772,
  title  = {On a Spectrum-level Splitting of the $BP \langle 2 \rangle$-Cooperations Algebra},
  author = {Elizabeth Ellen Tatum},
  journal= {arXiv preprint arXiv:2208.11772},
  year   = {2023}
}

Comments

Updated version: modified the construction of the splitting so that it now works at all primes. (the previous version was only for primes larger than 3)

On a Spectrum-level Splitting of the $BP \langle 2 \rangle$-Cooperations Algebra

Abstract

Keywords

Cite

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