Algebraic K-theory and the unstable homology of general linear groups

Abstract: The stable homology of general linear groups over a field is well-known to be closely related to its algebraic K-theory. I will discuss joint work with Soren Galatius and Oscar Randal-Williams which investigates the unstable homology of general linear groups. We will find it is closely related to the Milnor K-theory, by constructing a presentation of the disjoint union of $BGL_n(F)$ as an $\mathbb{E}_{\infty}$-algebra.

commutative algebraalgebraic geometryalgebraic topologygeometric topologyK-theory and homology

Audience: researchers in the topic

electronic Algebraic K-theory Seminar

Series comments: Description: Research seminar on algebraic K-theory