I am wondering if there is any computation of stable homotopy groups of $\mathbb{R}P^{\infty}\wedge \mathbb{R}P^{\infty}$ in low dimensions? I would be very grateful for any reference.



Tables for stable homotopy groups of $\mathbb{R}P^{\infty} \wedge \mathbb{R}P^{\infty}$
Bob Bruner and Christian Nassau both have code that can compute the Adams charts efficiently. For example, Bob has a chart for $\mathbb{R}P^2\wedge\mathbb{R}P^2$ at <http://www.rrb.wayne.edu/cohom/index.html>, and he might be able to do $\mathbb{R}P^\infty\wedge\mathbb{R}P^\infty$ with little effort if you asked him nicely. But I don't know where you would find information about the Adams differentials.


