Algebra/Topology Seminar

Speaker: Thomas Nikolaus

Title: A spherical HKR theorem

Abstract: We prove a version of the Hochschild-Kostant-Rosenberg theorem for any commutative spectrum A whose homotopy groups \pi_*(A) satisfy a certain smoothness condition relative to the homotopy groups of some base ring spectrum k. More precisely we show that the topological Hochschild homology groups THH_*(A) and the relative topological Hochschild homology groups THH_*(A/k) are under these assumptions given by \eta-deformed versions of the de Rham complex of \pi_*(A) relative to \pi_*(k). These deformations are described entirely algebraically in terms of certain power operations \eta_m: \pi_{2n}(A) --> \pi_{2n+1}(A).

This is joint work with Achim Krause.

The physical location of the seminar will be Auditorium 6. Due to the very low demand, from this talk on we will stop broadcasting talks via Zoom.