Topology Seminar

The "image-of-J" spectrum in the classical stable homotopy category has been well-studied; Bachmann–Hopkins defined its motivic analogue. In this talk, I will start with the classical story, and then move to the motivic version. I will talk about the effective slice computation of the motivic "image-of-J" spectrum over the real numbers. Unlike the classical case, the map from the motivic sphere is not surjective on homotopy groups. Still, it captures a regular pattern that appears in the R-motivic stable stems. This is joint work with Eva Belmont and Dan Isaksen.