Real cobordism, its norm and the dual Steenrod algebra

The real cobordism spectrum MU_R and its norms play a central role in the proof of the non-existence of classes of Kervaire invariant one by Hill, Hopkins and Ravenel. However, these spectra are still very mysterious and their equivariant homotopy groups are difficult to compute.

In this talk I will focus on the norm of real cobordism into C_4, and draw a connection between it and the dual Steenrod algebra spectrum HF_2 \smash HF_2 with C_2-action by conjugation.  Then I will discuss how computations on both sides help each other.

This is joint work with Lennart Meier.