Seminar

Bökstedt defined topological Hochschild homology (THH) before the advent of the modern categories of spectra in use today, and he had to invent some rather complicated coherence machinery to mimic the algebraic definition of Hochschild homology. It was thought that a "naive" definition of THH using a modern category of spectra could never give the correct equivariant homotopy type. We compare the Bökstedt smash product to the norm construction from the Hill-Hopkins-Ravenel proof of the Kervaire Invariant One problem, and use that to show that using the category of orthogonal spectra we do get a sensible definition of THH. This simplifies the foundations and makes it possible to define things like Adams operations on THH(A) and TC(A). This is joint work with Blumberg, Gerhardt, Hill, Lawson and Mandell.