Polynomial functors and algebraic K-theory

Geometry Topology Seminar
Monday, December 5, 2016 - 14:00
1 hour (actually 50 minutes)
Skiles 006
Harvard University
The Grothendieck group K_0 of a commutative ring is well-known to be a \lambda-ring: although the exterior powers are non-additive, they induce maps on K_0 satisfying various universal identities. The \lambda-operations are known to give homomorphisms on higher K-groups. In joint work in progress with Barwick, Glasman, and Nikolaus, we give a general framework for such operations. Namely, we show that the K-theory space is naturally functorial with respect to polynomial functors, and describe a universal property of the extended K-theory functor. This extends an earlier algebraic result of Dold for K_0.