English

On the $K(1)$-local homotopy of $\mathrm{tmf} \wedge \mathrm{tmf}$

Algebraic Topology 2019-08-07 v1

Abstract

As a step towards understanding the tmf\mathrm{tmf}-based Adams spectral sequence, we compute the K(1)K(1)-local homotopy of tmftmf\mathrm{tmf} \wedge \mathrm{tmf}, using a small presentation of LK(1)tmfL_{K(1)}\mathrm{tmf} due to Hopkins. We also describe the K(1)K(1)-local tmf\mathrm{tmf}-based Adams spectral sequence.

Keywords

Cite

@article{arxiv.1908.01904,
  title  = {On the $K(1)$-local homotopy of $\mathrm{tmf} \wedge \mathrm{tmf}$},
  author = {Dominic Leon Culver and Paul VanKoughnett},
  journal= {arXiv preprint arXiv:1908.01904},
  year   = {2019}
}