Topology and Geometric Group Theory Seminar

Hana Jia KongInstitute for Advanced Study
The image of J in the motivic stable homotopy category

Tuesday, March 22, 2022 - 1:00pm
Zoom

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.