Algebra/Topology seminar

Speaker: Cary Malkiewich

Title: The norm model of topological Hochschild homology, and an application to THH(DX)

Abstract: I will describe a new model for topological Hochschild homology (THH), due to Angeltveit et al, which builds on the celebrated work of Hill, Hopkins and Ravenel. This model seems to be useful for understanding subtle multiplicative properties of THH. In particular, it lets us interpret the THH of a commutative ring as the multiplicative norm into genuine S^1 spectra. I will use this model to create cyclotomic structures on duals and mapping spectra of cyclotomic spectra. This work also uses a new rigidity theorem for diagonal maps of orthogonal G-spectra, which is simple to state but somewhat surprising. As an application, we get that the "Atiyah duality" between THH(DX) and the free loop space LX is actually a duality of genuine S^1-spectra, suggesting deeper connections between Waldhausen's A(X) and K(DX).