## Topology Seminar: Ben Williams

- Date: 11/22/2017
- Time: 15:15

University of British Columbia

The A1 calculation of the 4th homotopy group of the 6,3-sphere and a conjecture of Suslin

The algebraic K-theory, due to Quillen, of a field is related to a theory defined by Milnor called Milnor K-theory and denoted K^M. In the 1980s, Andrei Suslin constructed a map K_n(F) -> K^M_n(F), and conjectured that the image was the subgroup (n-1)! K^M_n(F). He also proved the conjecture for n<=3. For n=5, we reinterpret the construction as a construction in the A1 homotopy groups of spheres and BGL, and by calculating these groups, show that the conjecture is true in this case as well. This represents part of a joint project with Aravind Asok, Jean Fasel and Kirsten Wickelgren.

ESB 4133 (PIMS Lounge)

Wed 22 Nov 2017, 3:15pm-4:15pm