Computer calculated Adams d₂ differentials

This repository contains data files generated by ext-rs pertaining to the secondary Steenrod algebra algorithm. This includes the d₂ differentials generated by the algorithm as well as other data useful for consuming this data.

The data is computed for various spectra, and the files for each spectrum are placed in a directory named after the spectrum. For convenience, each data file is suffixed with the name of the module. Unless otherwise indicated by the extension, all files are plain text files.

The data files are as follows:

d2: The d₂ differentials. If the target bidegree is empty, the differentials are omitted.

hidden: Hidden extensions by 1 by the corresponding class. We have 2, η, ν and σ extensions for the sphere and η extensions for C2.

inclusion: The map in Ext induced by the inclusion of the bottom cell. In the case of C2 ∧ Cη, we also have the inclusion of the bottom copy of C2.

projection: The map in Ext induced by projection to the cell. In the case of C2 ∧ Cη, we also have the projection to the top copy of C2.

filtration_one: A list of all filtration one products.

kappa: Product with κ. This is only available for the sphere.

kappabar: Product with \(\bar{\kappa}\). This is only available for the sphere.

change_of_basis: The correspondence between our basis and Bruner's basis. Each row expresses one of our basis element in terms of Bruner's basis. This is only available for the sphere.

charts.pdf: The Adams charts showing the d₂'s and the E₃ page, drawn by TikZ.

clean_charts.pdf: The same charts but without showing h₂ products.

charts.tex, clean_charts.tex: Source files for the above charts.

*.svg: Same charts in SVG format.

differentials.gz: The differentials in our minimal resolution, in a human-readable plain text format.

bruner.tar.gz: The differentials in our resolution, in Bruner's format.

module.json: Module definition files used by ext-rs.

num_gens: Number of generators in each bidegree. This is useful for further processing of data.

See arxiv:2105.07628 for more information about this dataset.