Algebraic Topology Seminar

(Joint work with Dominic Culver) Let kq denote the very effective cover of Hermitian K- theory.  The kq-based motivic Adams spectral sequence, or kq-resolution, is a motivic analog of Mahowalds bo-resolution. We applied the kq-resolution in the C-motivic setting to calculate the η-periodic stable stems (recovering results of Andrews, Guillou, Isaksen, and Miller) and v1-periodic stable stems. I will summarize these calculations and discuss work in progress towards analogous results over general base fields and in the C2-equivariant setting. In addition to large-scale calculations of periodic phenomena, the kq-resolution can be used to calculate low-dimensional 2-complete Milnor-Witt stems. I will present some calculations in the C- and R-motivic settings (recovering results of Dugger-Isaksen), then discuss work in progress towards analogous results over general base fields and the 2-complete version of calculations of Rndigs-Spitzweck- Østvaer.

For information, write: araminta@mit.edu