Geodesic
The $\mathsf{P}^1_2$ margolis homology of connective topological modular forms
Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 379-402.

Voir la notice de l'article provenant de la source International Press of Boston

The element $\mathsf{P}^1_2$ of the $\operatorname{mod}2$ Steenrod algebra $\mathcal{A}$ has the property $(\mathsf{P}^1_2)^2 = 0$. This property allows one to view $\mathsf{P}^1_2$ as a differential on $H_\ast (X, \mathbb{F}_2)$ for any spectrum $X$. Homology with respect to this differential, $\mathcal{M} (X, \mathsf{P}^1_2)$, is called the $\mathsf{P}^1_2$ Margolis homology of $X$. In this paper we give a complete calculation of the $\mathsf{P}^1_2$ Margolis homology of the $2$-local spectrum of topological modular forms tmf and identify its $\mathbb{F}_2$ basis via an iterated algorithm. We apply the same techniques to calculate $\mathsf{P}^1_2$ Margolis homology for any smash power of tmf.
DOI : 10.4310/HHA.2021.v23.n2.a21
Classification : 55N35, 55P42, 55S10, 55S20
Keywords: Steenrod algebra, Margolis homology, topological modular forms 
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Prasit Bhattacharya; Irina Bobkova; Brian Thomas. The $\mathsf{P}^1_2$ margolis homology of connective topological modular forms. Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 379-402. doi : 10.4310/HHA.2021.v23.n2.a21. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n2.a21/

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