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2 results for “Steenrod algebra”
Cohomology of the Mod 2 Steenrod algebra
<p>New version notes: The t column in the resolution csv table is corrected. It was identical to the id column.</p> <p>In this repo you will find the tables of the cohomology of the Mod 2 Steenrod algebra up to total degree of 261 in many formats, including pdf, csv files, and an interactive plot of the E2 page of the Adams spectral sequence on <a href="https://waynelin92.github.io/ss/index.html">link</a>. We also provide the Steenrod resolution data in the same range.</p> <p>In AdamsE2 csv files, "1,2,3,4;7,8" stands for $x_1^2x_3^4+x_7^8$ where $x_i$ is the i'th generator in the generator csv table with i as id. In the generator csv table, the res_id column corresponds to the id column of the representing elements in the resolution table.</p> <p>In the resolution csv table, each row "s,t,index,diff" means that in degree (s,t), d(v_{index})=diff. In the diff column, "1,2:3+4:5" stands for $P(1,2)v_3+P(4)v_5$ where $v_i$ is the generator of the free module in Adams filtration s-1 with index i.On the interactive plot, you can scroll the mouse wheel and drag to navigate. You can double click the dots to see the details about the elements.</p> <p>The author is supported by China Postdoctoral Science Foundation 2021TQ0015 and the Fundamental Research Funds for the Central Universities, Peking University.</p>
Secondary Steenrod algebra calculations
<p>This repository contains data files generated by <a href="https://zenodo.org/record/6329789">ext-rs</a> pertaining to the secondary Steenrod algebra algorithm. This supersedes <a href="https://zenodo.org/record/4766457">https://zenodo.org/record/4766457</a> but is not a strict superset of the data.</p> <p>This repository contains three files.</p> <ul> <li> <p><code>d2-data.zip</code> is a zip file containing the generated data, which are as follows:</p> <ul> <li><code>d2</code>: The d₂ differentials. If the target bidegree is empty, the differentials are omitted.</li> <li> <p><code>product_a</code>: The secondary product of all elements with <code>[a]</code>.</p> </li> <li> <p><code>massey_a_b</code>: The secondary Massey product <code><[a], [b], -></code>. The only exception is <code>massey_P</code> which contains the Adams periodicity operator <code><[h_3], [h_0^4], -></code>.</p> </li> <li> <p><code>filtration_one</code>: A list of all filtration one products.</p> </li> <li> <p><code>charts.pdf</code>: The Adams charts showing the d₂'s and the E₃ page, drawn by TikZ.</p> </li> <li> <p><code>clean_charts.pdf</code>: The same charts but without showing h₂ products.</p> </li> <li> <p><code>differentials.gz</code>: The differentials in our minimal resolution, in a human-readable plain text format.</p> </li> <li> <p><code>change_of_basis</code>: The correspondence between our basis and Bruner's basis in <a href="https://arxiv.org/abs/2109.13117">arXiv:2109.13117</a>. Each row expresses one of our basis element in terms of Bruner's basis.</p> </li> </ul> <p>Unless otherwise suggested by the file extension, all files are plain text (utf-8) files. The script and the save file are known to be compatible with the version of the code in <a href="https://zenodo.org/record/5898397">https://zenodo.org/record/5898397</a></p> </li> <li> <p><code>script.sh</code> is a script that generates the files above, except for <code>change_of_basis</code> and the charts. This is to be run in the `ext/` directory of <a href="https://zenodo.org/record/6329789">sseq</a>. If the execution of the script is interrupted halfway through, it is safe to simply run the script again with the safe parameters to resume computation; the vast majority of the computation would have been saved in the save directory and need not be recomputed (If a save file was corrupted due to the interruption, the program will panic instead of silently propagate errors). Similarly, the script can be run with a larger/different range and previous computations would be reused.</p> </li> <li> <p><code>S_2_milnor.tar</code> is an archive containing the algorithm's save file for the above computation, up to <code>(n, s) = (140, 72)</code>.</p> </li> </ul>
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