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arXiv · 1708.09568

The cohomology of $C_2$-equivariant $A(1)$ and the homotopy of $ko_{C_2}$

Bertrand J. Guillou·Michael A. Hill·Daniel C. Isaksen·Douglas C. Ravenel
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Abstract

We compute the cohomology of the subalgebra $A^{C_2}(1)$ of the $C_2$-equivariant Steenrod algebra $A^{C_2}$. This serves as the input to the $C_2$-equivariant Adams spectral sequence converging to the $RO(C_2)$-graded homotopy groups of an equivariant spectrum $ko_{C_2}$. Our approach is to use simpler $\mathbb{C}$-motivic and $\mathbb{R}$-motivic calculations as stepping stones.

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Bertrand J. Guillou, Michael A. Hill, Daniel C. Isaksen, Douglas C. Ravenel. 2017-08-31. The cohomology of $C_2$-equivariant $A(1)$ and the homotopy of $ko_{C_2}$. https://doi.org/10.2140/tunis.2020.2.567

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