BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ben Williams (University of British Columbia) DTSTART:20201207T154000Z DTEND:20201207T163000Z DTSTAMP:20260422T135607Z UID:BilTop/6 DESCRIPTION:Title: A 1 homotopy groups of GL_n and a problem of Suslin's\nby Ben Williams ( University of British Columbia) as part of Bilkent Topology Seminar\n\nLec ture held in SB-Z11.\n\nAbstract\nLet $F$ be an infinite field. Andrei Sus lin constructed a morphism from the (Quillen) K-theory of $F$ to the Milno r K-theory of $F$: $s_n : K_n(F) \\to K_n^M(F)$. He proved that the image of $s_n$ contains $(n-1)! K_n^M(F)$. He raised the question of whether thi s accounted for the whole image—it was known to when $n$ is $1$\, $2$ or $3$. In this talk I will explain how one can partially recover this morph ism as a morphism of $A^1$-homotopy groups of down-to-earth objects\, and I will show how this tells us some things about Suslin's question when $n$ is $4$ and settles it when $n$ is $5$. This talk represents joint work wi th Aravind Asok and Jean Fasel.\n LOCATION:https://researchseminars.org/talk/BilTop/6/ END:VEVENT END:VCALENDAR