Computing the homology of the motivic lambda algebra.

The classical lambda algebra is a differential graded algebra, whose homology is the \(E_2\) page of the Adams spectral sequence computing the stable homotopy groups of spheres. I investigated generalizations of the Curtis algorithm, an inductive process for computing this homology, to determining motivic Adams \(E_2\) pages.

I have been writing some code to help with various computations in the classical, \(\mathbb{C}\)-motivic, and \(\mathbb{R}\)-motivic lambda algebras. I’ve managed to use the Curtis algorithm to automate the generation of classical Adams charts, in the style of Isaksen, Wang and Xu; I’m currently working on automating the generation of \(\mathbb{C}\)-motivic charts.

A Github repository containing some of my code is available here; currently rough and uncommented, but I plan on adding a manual soon. If you want to use it, feel free to let me know and I can get you started.

A draft of a paper describing some of my work is available here. Here, I give a description of the classical Curtis algorithm, and present a \(\mathbb{C}\)-motivic generalization. Still rough, but any comments are welcome!